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This unit introduces students to four ways of solving quadratic equations, graphing, factoring, completing the square, and the quadratic formula. The instructor uses Two-Column Notes and Triple-Entry Vocabulary Journals to support student learning and build comprehension. Knowledge Rating Guides serve as self assessments for the students, both before and after the unit. To integrate technology into the unit, the instructor utilizes Geogebra, free mathematics software that can be downloaded at
LEARNING AND INSTRUCTIONAL GOALS
ENDURING UNDERSTANDINGS: How and why quadratic equations are used. How to determine which method of solving is best to use given the situation.
ESSENTIAL QUESTIONS How are quadratic equations used in the "real" world? What are the different ways to solve quadratic equations and when is each appropriate?
STUDENTS WILL KNOW/UNDERSTAND: Students will develop several ways to solve quadratic equations and be able to decide which way is appropriate to the situation.
STUDENTS WILL BE ABLE TO: Use Two-column Notes to help organize questions from each section and then use them to help review for the final assessment. Use Triple Entry Vocabulary Journals to learn vocabulary and to demonstrate mastery of terms. This will be added to the previous unit's vocabulary to construct a vocabulary digital notebook from year to year. Knowledge Rating Guide at beginning of unit to activate previous knowledge and at end to reinforce important words and concepts.
MAINE LEARNING RESULTS/NCTM:
MAINE
Real numbers:
1b, estimate the value(s) of roots and use technology to approximate them.
1e, understand that some quadratic equations do not have real solutions and that there exist other number systems to allow for solutions to these equations.
Equations and inequalities:
2b, solve quadratic equations graphically, by factoring in cases where factoring is efficient, and by applying the quadratic formula.
Functions and relations:
4a, recognize the graphs and sketch graphs of the basic functions.
4b, apply functions from these families to problem situations.
4c, use concepts such as domain, range, zeros, intercepts, and maximum and minimum values.
FORMATIVE: Pre-assessment to help activate prior knowledge and help determine length of time needed to spend on each section of the unit. The results will help the instructor to assess whether students have retained knowledge on factoring and graphing to help determine if extra time will be needed to review these topics.
Knowledge Rating Guide will also offer instructor insight into what vocabulary should be reinforced and which is completely new and will need introduction.
Homework will offer insight into students' understanding of class information, and will inform teacher if students are ready to move on or need more practice.
Exit Slips to help instructor assess each day's lessons and concepts.
SUMMATIVE:
Two quizzes will be given during the unit. The first after the first two sections and the second after the third and fourth sections. Quizzes will also help inform instruction by indicating if more time needs to be spent on the material that is covered on the quiz.
The post-assessment, which will have similar questions to the pre-assessment, will be used to show the growth of the students' understanding throughout the unit.
TECHNOLOGY INTEGRATION
NeoOffice will be used as students build their high school math digital notebooks. These notebooks will help students to organize and study. Students will have each unit's vocabulary, Two-column Notes for review, and Knowledge Rating Guides. These tools are used throughout the unit.
Geogebra will be used to help students visualize quadratic equations. Students will also be able to easily manipulate and create multiple representations of the material, which will help reinforce the lessons as well as give students multiple opportunities to analyze the graphs and how they relate to the given situations in the problems.
LITERACY SUPPORT
Students will be expected to recognize quadratic functions and be able to discuss and understand different ways to solve these functions. They will also then need to evaluate which method is appropriate for the given situation.
The literacy skills required will be two types of note taking, which are a Triple Entry Vocabulary Journal and Two-column Notes. Students will also use a Knowledge Rating Guide to activate prior knowledge and then to access their learning at the end of the unit.
Model for students using LCD projector and Smart Board the use of the digital versions of Triple Entry Vocabulary Journal and Two-column Notes. Using a gradual release method, students will take ownership of these tools for themselves.
Exit Slips and Knowledge Rating Guides are used in other classes, so just reinforce their use and importance in the learning environment.
This unit follows the unit on polynomials and deepens student's understanding of specifically quadratic polynomials and how they may encounter them. The unit following this deals with other polynomial functions.
Quadratic functions are used to model real life situations and data.
Students need to be familiar with graphing functions, simplifying rational expressions, and multiplying and factoring polynomial expressions.
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Most Helpful Customer Reviews
Although this book was written with the BBC Micro in mind, the mathematics can easily be applied to any computer. I bought this book primarily for the 3D graphics and this book would be useful for anyone wanting to know the nuts and bolts of 3D graphics. All the necessary code is given in the book and can be a little hard to disambiguate as it is written in a modular style which means you have to keep refering back to earlier pages, but this is easy enough to figure out. The text is complete and not too dry to read and the accompanying diagrams are helpful. You will not find how to draw the camera or the car (shown on the cover) in this book but by the end of it you will know how to. 3D graphics is covered in the following chapters- 3. Two-Dimensional Coordinate Geometry 4. Matrix Representation of Transformation on Two-dimensional Space 7. Three-dimensional Coordinate Geometry 8. Matrix Representation of Transformations on Three-dimensional Space 9. Orthographic Projections Chapters 10 and 12 cover hidden line removal and chapter 11 covers Perspective and Sterescopic Perspective As a sign of the times the book was written the following passage from the section on Hidden Surface and Hidden Line removal after showing us how to draw a complex cube(with 120 facets) which takes a quarter of an hour to draw:- "We have reached the limits of three-dimensional graphics on the BBC Model B microcomputer. You must use larger computers if you wish to go further in your study of this type of computer graphics" !
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Summary
The BPB team has created a book where the use of the graphing calculator is optional but visualizing the mathematics is not. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition to helping students visualize the math with side-by-sides, the authors focus on helping students make the connection between x-intercepts, zeros, and solutions, both visually and algebraically.
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FREE PRODUCTS
Secondary
These products are intended for grades 7 through 12. Depend on the Algebra Survival Guide to introduce algebra concepts in a way that helps students truly "get it". Offer the Guide to children before they enter Algebra 1 or as a translation tool to help students understand a confusing Algebra 1 textbook. Great for English Language Learners because the text is conversational and educational cartoons provide a visual way to grasp tricky algebra concepts.
College and Beyond
Are you an adult putting off going to college because of algebra anxiety? If so, the Algebra Survival Guide uses humor, conversational language, step-by-step instructions and lots of practice problems to ensure you finally understand basic algebra concepts. The Workbook offers hundreds more practice problems. Once you thoroughly grasp these concepts, you'll be well on your way to algebra success.
Welcome!
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Check out some quotes below ...
"I'm a returning college adult now in the fourth week of my College Algebra course. The Algebra Survival Guide has FINALLY filled in the gaps in my earlier education. Thank you to the third power. Thirty years of math phobia gone in three hours of reading."
— Mary Ellen Kirian, Lake Oswego, OR
The Best Algebra teaching guide yet!
After searching for over a year, I finally found the book that helps me and my son understand algebra. I have never in my entire life gotten higher than a C- in algebra and have gotten plenty of fails, but with this book I completely understand the concept AND can explain it to my son so that he gets the correct conclusions. He works with it on his own without getting frustrated like he was with the other books. It is a fun and slow paced book with just enough to practice on before you move to the worksheets. I am glad I purchased this book.
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| 677.169 | 1 |
An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and pre-college calculus. Logarithms and Exponential; Sequences; Series; Techniques of...
This field guide contains a quick look at the functions commonly encountered in single variable calculus, with exercises for each topic: linear, polynomial, power, rational, exponential, logarithmic, trigonometric, and...
A unit that addresses the sheer volume of incomprehensible numbers (speed, distance, age) in the natural world, helping students to understand the scale of the world using the concepts of rates, proportions and...
Links to selected sites, projects, and graphing calculator explorations designed to foster understanding of the family of functions known as exponential functions, useful in such applications as population growth,...
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This ebook is available for the following devices:
iPad
Windows
Mac
Sony Reader
Cool-er Reader
Nook
Kobo Reader
iRiver Story
more
Your hands-on guide to real-world applications of linear algebra
Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.
Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
| 677.169 | 1 |
An essential subject for all learners, Cambridge IGCSE Mathematics encourages the development of mathematical knowledge as a key life skill, and as a basis for more advanced study. The syllabus aims to build learners' confidence by helping them develop a feel for numbers, patterns and relationships, and places a strong emphasis on solving problems and presenting and interpreting results. Learners also gain an understanding of how to communicate and reason using mathematical concepts.
Please note: June 2016 is the final examination series in which syllabus 0580 will be funded in state schools. After 2016 it will be unregulated and unfunded. Schools wishing to continue to offer a regulated and funded version should move to our new Cambridge IGCSE (9-1) Mathematics (0626). This new syllabus will not count in government performance tables.
You can download one or more question papers for a previous session. Teachers registered with Cambridge can access our password-protected Teacher Support site, where a much wider selection of syllabus materials is available to download.
Syllabuses
The syllabus year refers to the year in which the examination will be taken.
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Valley Glen, CA PrecalculusAdding i into the mix allows you to take the square root of any real number. (This notion of ?expanding the space of mathematics? is a common theme in the history of mathematics. In a way it?s a search for completeness and ? though it often turns out to be useful ? it is usually pursued for its...Because It is also a fun challenge to teach a student to think outside of the box.
...With a well-built foundation, progress to the next level is easy and natural. The alternative usually results in much struggle until the fundamentals are finally learned or the student gives up and barely scrapes by. The ability to easily use algebra is essential for success in chemistry, biology, physics, economics and many other classes and professions.
| 677.169 | 1 |
Developmental Math
Developmental Mathematics
Developmental Mathematics courses are pre-curriculum level courses intended to prepare
students for the college level math courses required in their curriculum programs.
The goal of Developmental Mathematics is to aid students in gaining the knowledge,
self-confidence, problem-solving experience, and study skills they need to be successful
in college-level mathematics.
Modular Courses:
The Developmental Math (DMA) courses are broken down into four-week modules. There
are 8 modules: DMA 010, DMA 020, DMA 030, DMA 040, DMA 050, DMA 060, DMA 070, and
DMA 080. Where you start is determined by your placement test score or an evaluation
of your scholastic records by the admissions staff. To determine the modules you need
to complete for your curriculum program, go to What Math Do I Need? under the FAQs section in the lower right column on this page.
Which Format is for Me?
There are three different methods of delivery for pre-curriculum math courses: Face-to-Face
classes (DMA), Customizable Learning (DMS), and Online (DMA). In each format, students
complete online homework assignments to prepare for the module posttest. The face-to-face
format provides traditional classroom instruction. Customizable learning courses are
technology-rich classes held in a computer lab. Although there is an instructor present
at all times to answer questions and assist students, the customizable learning format
gives students the opportunity to work at their own pace through one or more modules
they need to complete. The online format works like a typical internet class, except
for the required posttest. Students in an online course must take their posttest
in person, rather than over the internet. The option to use a local proctor is available
to students in the online course who live too far away to travel to main campus.
How Do I Register for Developmental Math?
If you are currently taking a pre-curriculum math class, your instructor will assist
you in registering for the next module you need to complete. If not, your program
advisor can assist you or you may visit the Math Department, located in room 618 of
Horace Sisk, for help with registration.
Tools Required for Developmental Math:
To be successful in a pre-curriculum math course, you will need the following tools:
Developmental G.O.A.L. Math Workbook, available through the FTCC bookstore.
Access to a computer with internet access, either at home or through FTCC's Open Computer
Lab.
Calculator - to determine the type needed for your course, go to Which Calculator? under the FAQs section on this page.
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provided under a Creative
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Commons license.
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OpenCourseWare continue to
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To make a donation, or to view
additional materials from
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hundreds of MIT courses, visit
MIT OpenCourseWare
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at ocw.mit.edu.
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PROFESSOR STRANG: So this
is the first true review
10
00:00:24 --> 00:00:27
session in 18.085.
11
00:00:27 --> 00:00:32
The last Wednesday, the first
Wedneday afternoon was a
12
00:00:32 --> 00:00:38
brief review of topics
in linear algebra.
13
00:00:38 --> 00:00:40
But now we're into the course.
14
00:00:40 --> 00:00:44
We've done four lectures on the
first four sections of the
15
00:00:44 --> 00:00:50
textbook and one homework
problem in and back and a
16
00:00:50 --> 00:00:54
second homework set
for next Monday.
17
00:00:54 --> 00:00:58
So I'm ready for any questions,
including questions that are
18
00:00:58 --> 00:01:00
on the homework if necessary.
19
00:01:00 --> 00:01:03
But anything at all.
20
00:01:03 --> 00:01:08
Or maybe I'll just ask
whether the pace, so
21
00:01:08 --> 00:01:09
this is really informal.
22
00:01:09 --> 00:01:13
Is the pace of the course, now
today's lecture had a lot in it
23
00:01:13 --> 00:01:17
as I realized when I saw that
the board with still full of
24
00:01:17 --> 00:01:22
18.085 and there was a little
more still to do because we
25
00:01:22 --> 00:01:26
didn't finish the matrix part.
26
00:01:26 --> 00:01:33
But are you ok with the sort
of speed of the course?
27
00:01:33 --> 00:01:34
So that'll be one question.
28
00:01:34 --> 00:01:39
And then, what about specifics?
29
00:01:39 --> 00:01:42
Somebody start off if you will.
30
00:01:42 --> 00:01:42
Anybody.
31
00:01:42 --> 00:01:43
Yes, thanks.
32
00:01:43 --> 00:01:46
AUDIENCE: Well, actually I
had a question about the
33
00:01:46 --> 00:01:47
lecture earlier today.
34
00:01:47 --> 00:01:49
PROFESSOR STRANG:
Okay, go ahead.
35
00:01:49 --> 00:01:51
AUDIENCE: I was just going to
look it up in the text, but.
36
00:01:51 --> 00:01:52
PROFESSOR STRANG:
That's alright.
37
00:01:52 --> 00:01:54
AUDIENCE: But haven't
had a chance to.
38
00:01:54 --> 00:01:58
But, ok, so I'm not really sure
how you take the initial
39
00:01:58 --> 00:02:02
conditions and apply them
to the ramp function to
40
00:02:02 --> 00:02:04
actually get a solution.
41
00:02:04 --> 00:02:09
PROFESSOR STRANG: So that's
what luckily happens to be
42
00:02:09 --> 00:02:11
still here on the board, right?
43
00:02:11 --> 00:02:14
We've got these boundary,
I would call them
44
00:02:14 --> 00:02:16
boundary conditions.
45
00:02:16 --> 00:02:19
So this is definitely, we're in
a part of math that's about
46
00:02:19 --> 00:02:23
boundary value problems more
than time, isn't
47
00:02:23 --> 00:02:24
in the picture.
48
00:02:24 --> 00:02:28
I mean later time will
get into the picture.
49
00:02:28 --> 00:02:37
So with this particular
example, the general solution
50
00:02:37 --> 00:02:44
is a standard ramp at the point
a where things are happening.
51
00:02:44 --> 00:02:47
Plus the C+Dx, the usual.
52
00:02:47 --> 00:02:50
So that's a
particular solution.
53
00:02:50 --> 00:02:54
That particular solution
has the right behavior
54
00:02:54 --> 00:02:59
at the impulse.
55
00:02:59 --> 00:03:04
By the right behavior, I mean
that the second derivative of
56
00:03:04 --> 00:03:10
the ramp is a delta and when I
put the ramp at a, then the
57
00:03:10 --> 00:03:12
delta will show up at a.
58
00:03:12 --> 00:03:16
And when I put on that minus
sign it'll mean that the second
59
00:03:16 --> 00:03:19
derivative is minus the delta.
60
00:03:19 --> 00:03:23
So the slope will step down.
61
00:03:23 --> 00:03:24
So that's a
particular solution.
62
00:03:24 --> 00:03:31
But that by itself, what
does that equal at zero?
63
00:03:31 --> 00:03:36
And what does that equal at
one if you remember the ramp?
64
00:03:36 --> 00:03:38
So let me just draw
that ramp again.
65
00:03:38 --> 00:03:44
So the ramp was really based
on, centered at the point a.
66
00:03:44 --> 00:03:46
And I'll put it
with a minus sign.
67
00:03:46 --> 00:03:50
So it came along there
and down there.
68
00:03:50 --> 00:03:53
And now suppose this is one
end of our interval and
69
00:03:53 --> 00:03:56
that's the other end.
70
00:03:56 --> 00:03:59
So is that ramp the
answer to our problem?
71
00:03:59 --> 00:04:00
No.
72
00:04:00 --> 00:04:06
Well it happens to satisfy this
boundary condition, happens
73
00:04:06 --> 00:04:08
to start out at zero.
74
00:04:08 --> 00:04:10
But it doesn't end up at zero.
75
00:04:10 --> 00:04:19
So just like every particular
solution we need a little more.
76
00:04:19 --> 00:04:22
We have to include more
solutions because
77
00:04:22 --> 00:04:24
that was only one.
78
00:04:24 --> 00:04:26
All those are equally
good solutions.
79
00:04:26 --> 00:04:30
If I add C+Dx, the second
derivative of that is
80
00:04:30 --> 00:04:33
zero, so it doesn't
spoil anything at all.
81
00:04:33 --> 00:04:38
On the contrary, it
adds more solutions.
82
00:04:38 --> 00:04:42
I mean the great thing we're
using here is that our
83
00:04:42 --> 00:04:49
equations are linear and when
zero's on the right-hand
84
00:04:49 --> 00:04:51
side-- notice there's
no arbitrary constant.
85
00:04:51 --> 00:04:53
I'm not putting an
arbitrary constant on
86
00:04:53 --> 00:04:55
that particular solution.
87
00:04:55 --> 00:05:01
Is one particular solution
plus a subspace if I
88
00:05:01 --> 00:05:02
use that language.
89
00:05:02 --> 00:05:09
A lot of solutions to the, all
the solutions to the problem
90
00:05:09 --> 00:05:10
with zero on the
right-hand side.
91
00:05:10 --> 00:05:14
And these are the solutions,
these are the null space guys,
92
00:05:14 --> 00:05:19
the ones that have zero
on the right-hand side.
93
00:05:19 --> 00:05:22
Now we need those.
94
00:05:22 --> 00:05:27
And the effect of those
will be to move that ramp.
95
00:05:27 --> 00:05:29
And effectively, what
are they going to do?
96
00:05:29 --> 00:05:33
They're going to swing that
ramp around, it'll stay a ramp.
97
00:05:33 --> 00:05:36
But instead of being
level here, it'll go up.
98
00:05:36 --> 00:05:41
And instead of going down
there, it'll go down there.
99
00:05:41 --> 00:05:44
It'll be the same ramp,
with still that slope
100
00:05:44 --> 00:05:46
dropped by one.
101
00:05:46 --> 00:05:52
Slope went down by minus
one and that's not
102
00:05:52 --> 00:05:53
going to change here.
103
00:05:53 --> 00:05:59
The slope will still
go down by minus one.
104
00:05:59 --> 00:06:03
But now I've just adjusted
it so that it goes through
105
00:06:03 --> 00:06:06
the, it satisfies the
boundary conditions.
106
00:06:06 --> 00:06:11
And in the second problem
with the free end,
107
00:06:11 --> 00:06:14
again, here's my ramp.
108
00:06:14 --> 00:06:16
But now I'm going to adjust it.
109
00:06:16 --> 00:06:17
And what happened?
110
00:06:17 --> 00:06:20
It just needed
adjustment upwards.
111
00:06:20 --> 00:06:26
Because this was the zero,
this was the u=0 fixed guy.
112
00:06:26 --> 00:06:32
And now if I'm doing u'(0)=0,
the free guy, I can lift
113
00:06:32 --> 00:06:33
the whole thing up.
114
00:06:33 --> 00:06:37
So you see, I just lifted it
up to the point where it
115
00:06:37 --> 00:06:39
came out right there.
116
00:06:39 --> 00:06:43
So in this case I
just needed a C.
117
00:06:43 --> 00:06:45
And in this case I
just needed a Dx.
118
00:06:46 --> 00:06:49
And in other cases I
might have needed both.
119
00:06:49 --> 00:06:51
A little bit of C
and a little of Dx.
120
00:06:51 --> 00:06:59
Anyway that's what was, maybe
that's sort of repeating what
121
00:06:59 --> 00:07:02
we did today a little bit.
122
00:07:02 --> 00:07:08
But mechanically it's just,
we've got a particular solution
123
00:07:08 --> 00:07:14
and we've got the complete
solution and then we just have
124
00:07:14 --> 00:07:18
to choose C and D and we've got
two conditions to do it with,
125
00:07:18 --> 00:07:20
the two boundary conditions.
126
00:07:20 --> 00:07:22
Could have other
boundary conditions.
127
00:07:22 --> 00:07:26
Now, what about,
here's a, yeah.
128
00:07:26 --> 00:07:29
I guess what will often happen
in these review sessions is I
129
00:07:29 --> 00:07:33
get on a roll and I just
keep, carry on with it.
130
00:07:33 --> 00:07:37
You know, you start me with a
question and I can't stop.
131
00:07:37 --> 00:07:42
So I'll go a little longer
but then I really will stop,
132
00:07:42 --> 00:07:45
ready for the next one.
133
00:07:45 --> 00:07:50
So we haven't discussed
the free-free. u(0)
134
00:07:50 --> 00:07:52
u', sorry, free is u'.
135
00:07:53 --> 00:08:00
That's free at the left
and free at the right.
136
00:08:00 --> 00:08:04
What's up with that?
137
00:08:04 --> 00:08:06
What's the solution to that?
138
00:08:06 --> 00:08:13
Again, I'm looking for
-u'' equal an impulse.
139
00:08:13 --> 00:08:16
With those two boundary
conditions, free-free.
140
00:08:16 --> 00:08:19
And do you know what's
going to happen?
141
00:08:19 --> 00:08:22
No solution.
142
00:08:22 --> 00:08:25
Now it'd be interesting
to see why not.
143
00:08:25 --> 00:08:28
Why no solution?
144
00:08:28 --> 00:08:32
Well one way to do it is try.
145
00:08:32 --> 00:08:36
Other right-hand sides
could have a solution.
146
00:08:36 --> 00:08:41
So it's not just that this is
something the matter here.
147
00:08:41 --> 00:08:44
Specifically, that right-hand
side and most right-hand
148
00:08:44 --> 00:08:46
sides will fail.
149
00:08:46 --> 00:08:47
But let's just see
it with this one.
150
00:08:47 --> 00:08:50
Why does that fail?
151
00:08:50 --> 00:08:57
Well you can see I can't, the
slope here is zero and the
152
00:08:57 --> 00:08:59
slope here is minus one.
153
00:08:59 --> 00:09:06
If I adjust those I can't get,
this is asking me to get
154
00:09:06 --> 00:09:07
slope zero at both ends.
155
00:09:07 --> 00:09:10
I can't do that, right?
156
00:09:10 --> 00:09:15
Yeah, just not
possible for me to.
157
00:09:15 --> 00:09:19
This will add a straight line
but it's the same straight.
158
00:09:19 --> 00:09:23
I can't get a ramp that comes
flat at both ends because
159
00:09:23 --> 00:09:28
there's, once I say what it's
doing at the ends, I've got it.
160
00:09:28 --> 00:09:31
And you see what I mean?
161
00:09:31 --> 00:09:41
I'm looking for one that starts
flat and ends flat and that's
162
00:09:41 --> 00:09:45
not in my family of solutions.
163
00:09:45 --> 00:09:49
That problem just doesn't
have a solution.
164
00:09:49 --> 00:09:53
So that's one way to do it is
look at the solutions and
165
00:09:53 --> 00:09:56
realize you can't satisfy
both boundary conditions.
166
00:09:56 --> 00:10:00
Another way might be this.
167
00:10:00 --> 00:10:05
This is a little bit deeper
way and it leads to
168
00:10:05 --> 00:10:07
something better.
169
00:10:07 --> 00:10:10
Suppose I take the integral.
170
00:10:10 --> 00:10:13
So this is an equation
that's supposed to hold.
171
00:10:13 --> 00:10:18
Let me integrate both
sides from zero to one.
172
00:10:18 --> 00:10:21
So there's the idea
I'm putting in now.
173
00:10:21 --> 00:10:23
To go a little further,
to discover when
174
00:10:23 --> 00:10:25
this has a solution.
175
00:10:25 --> 00:10:28
Or let me take more
generally, -u''=f(x).
176
00:10:28 --> 00:10:31
177
00:10:31 --> 00:10:33
So some other load.
178
00:10:33 --> 00:10:37
Not necessarily a point load,
not necessarily a uniform load,
179
00:10:37 --> 00:10:39
but maybe some other load.
180
00:10:39 --> 00:10:44
And now my boundary conditions,
I'm trying to do free-free.
181
00:10:44 --> 00:10:48
And usually no solution.
182
00:10:48 --> 00:10:52
But let's just see why and when
there might be a solution.
183
00:10:52 --> 00:11:02
The key idea is integrate
from zero to one.
184
00:11:02 --> 00:11:04
What do I get on the
right-hand side?
185
00:11:04 --> 00:11:10
Well, I get the integral of f,
whatever it is, and I would
186
00:11:10 --> 00:11:15
call that the total load.
187
00:11:15 --> 00:11:16
Fair enough?
188
00:11:16 --> 00:11:22
The total load of if it was a
delta function, the total load
189
00:11:22 --> 00:11:24
would be one and it would
be all in one spot.
190
00:11:24 --> 00:11:29
If it was uniformly over the
whole interval, well I guess
191
00:11:29 --> 00:11:32
that would also integrate
to one, so the total load
192
00:11:32 --> 00:11:33
would be one spread out.
193
00:11:33 --> 00:11:37
But it could be a mixture
of the two, could be a few
194
00:11:37 --> 00:11:39
delta functions, whatever.
195
00:11:39 --> 00:11:45
What happens when I integrate
the left side from zero to one?
196
00:11:45 --> 00:11:46
Can you do that one?
197
00:11:46 --> 00:11:47
The integral from zero to one.
198
00:11:47 --> 00:11:50
There's that dopey
minus sign. u''dx.
199
00:11:52 --> 00:11:55
What do I get?
200
00:11:55 --> 00:11:59
Why do I say that's
a good idea?
201
00:11:59 --> 00:12:04
If I integrate the second
derivative I get the
202
00:12:04 --> 00:12:05
first derivative.
203
00:12:05 --> 00:12:07
The integral of the second
derivative will be the first
204
00:12:07 --> 00:12:11
derivative with the minus.
205
00:12:11 --> 00:12:13
So it's minus the
first derivative.
206
00:12:13 --> 00:12:16
And what do I do now?
207
00:12:16 --> 00:12:18
I plug in the end
points, right?
208
00:12:18 --> 00:12:19
You integrate.
209
00:12:19 --> 00:12:20
I'm integrating zero to one.
210
00:12:20 --> 00:12:22
So I've found the integral.
211
00:12:22 --> 00:12:26
I've put zero to one in there.
212
00:12:26 --> 00:12:27
So what is that?
213
00:12:27 --> 00:12:33
That's minus the derivative
at one plus the
214
00:12:33 --> 00:12:40
derivative at zero.
215
00:12:40 --> 00:12:42
And now, what's that?
216
00:12:42 --> 00:12:44
That's zero.
217
00:12:44 --> 00:12:47
By my boundary
conditions, that's zero.
218
00:12:47 --> 00:12:49
So what have I found?
219
00:12:49 --> 00:12:52
I've found that if these are
the boundary conditions, then
220
00:12:52 --> 00:12:57
when I integrate the left side
it's going to give me zero.
221
00:12:57 --> 00:13:03
So when, what loads
could be ok?
222
00:13:03 --> 00:13:14
What loads f(x) could allow
me to solve this equation?
223
00:13:14 --> 00:13:19
The condition will be I need,
what do I need for the
224
00:13:19 --> 00:13:24
total load to be able
to solve this equation?
225
00:13:24 --> 00:13:28
The integral of the left side
was zero so the integral of the
226
00:13:28 --> 00:13:31
right side had better be zero.
227
00:13:31 --> 00:13:34
So that's the condition.
228
00:13:34 --> 00:13:36
If I have these boundary
conditions, then my
229
00:13:36 --> 00:13:38
problem is singular.
230
00:13:38 --> 00:13:40
Usually no solution.
231
00:13:40 --> 00:13:42
It's like having a
singular matrix.
232
00:13:42 --> 00:13:45
It's like having this
particular singular
233
00:13:45 --> 00:13:46
matrix, of course.
234
00:13:46 --> 00:13:48
Whoops, not that one.
235
00:13:48 --> 00:13:51
Let me get the plus sign
in the right position.
236
00:13:51 --> 00:13:52
That's a plus.
237
00:13:53 --> 00:13:57
-1; -1, 2, -1; -1, 1.
238
00:13:57 --> 00:13:59
Right?
239
00:13:59 --> 00:14:08
This is the discrete version
with a zero slope at both ends.
240
00:14:08 --> 00:14:10
It's our T matrix.
241
00:14:10 --> 00:14:12
No, what matrix is it?
242
00:14:12 --> 00:14:14
B.
243
00:14:14 --> 00:14:18
It's our B matrix, both ends.
244
00:14:18 --> 00:14:22
I'll just come back here and
then I'll do the discrete one.
245
00:14:22 --> 00:14:26
So tell me a load that
we could handle?
246
00:14:26 --> 00:14:30
A load we could handle.
247
00:14:30 --> 00:14:32
So the integral has to be zero.
248
00:14:32 --> 00:14:39
So suppose my load has
a delta function at a.
249
00:14:39 --> 00:14:42
Well that integral is one.
250
00:14:42 --> 00:14:46
So can you fix that, change
that load or do something,
251
00:14:46 --> 00:14:53
maybe put on another load to
get a total load of zero?
252
00:14:53 --> 00:14:55
What shall I do?
253
00:14:55 --> 00:14:59
Add another guy
with a minus sign.
254
00:14:59 --> 00:15:05
In other words, maybe
this, a delta function
255
00:15:05 --> 00:15:07
at some other point B.
256
00:15:07 --> 00:15:08
Well, that would do it.
257
00:15:08 --> 00:15:11
I believe we could
solve that problem.
258
00:15:11 --> 00:15:18
Even with these bad
boundary conditions.
259
00:15:18 --> 00:15:20
We could solve that problem.
260
00:15:20 --> 00:15:23
Because the total load would be
one from that, minus one from
261
00:15:23 --> 00:15:27
that, the total load
would be zero.
262
00:15:27 --> 00:15:30
In other words, what would
are solution look like?
263
00:15:30 --> 00:15:32
It has to start
with zero slope.
264
00:15:32 --> 00:15:37
So it would buzz alone
to a and then after b.
265
00:15:37 --> 00:15:40
And what does it
have to do here?
266
00:15:40 --> 00:15:48
If I graph the solution to this
guy from zero to one it starts
267
00:15:48 --> 00:15:51
with, it's free, so nothing's
happening until I get to a.
268
00:15:51 --> 00:15:55
Then what has to happen?
269
00:15:55 --> 00:16:01
Let's see, if I'm graphing
u, it'll be ramp.
270
00:16:01 --> 00:16:01
Right?
271
00:16:01 --> 00:16:02
It'll be a ramp, yeah.
272
00:16:02 --> 00:16:04
Because I've two derivatives.
273
00:16:04 --> 00:16:11
And it has to ramp down by one,
so it'll ramp whatever it does.
274
00:16:11 --> 00:16:15
I don't know where it stops.
275
00:16:15 --> 00:16:16
Where does it?
276
00:16:16 --> 00:16:18
Wait a minute.
277
00:16:18 --> 00:16:21
I haven't practiced this.
278
00:16:21 --> 00:16:26
So I start from the other end.
279
00:16:26 --> 00:16:31
The other end is flat.
280
00:16:31 --> 00:16:33
What's up?
281
00:16:33 --> 00:16:36
They gotta meet here.
282
00:16:36 --> 00:16:38
Oh, the other end is
flat, but not at zero!
283
00:16:38 --> 00:16:39
Dumb, stupid.
284
00:16:39 --> 00:16:40
Right.
285
00:16:40 --> 00:16:41
Ok.
286
00:16:41 --> 00:16:43
Yes, the other end
is flat, right.
287
00:16:43 --> 00:16:45
And it's, oh yeah, look!
288
00:16:45 --> 00:16:46
Oh, wonderful.
289
00:16:46 --> 00:16:47
You see.
290
00:16:47 --> 00:16:53
That slope dropped by one and
the slope there increased
291
00:16:53 --> 00:16:55
by one back to zero.
292
00:16:55 --> 00:16:56
Slope was zero.
293
00:16:56 --> 00:17:00
It dropped to minus one
because of that load.
294
00:17:00 --> 00:17:03
Now it increased back to
zero because of this load
295
00:17:03 --> 00:17:07
with the minus sign and
there's a solution.
296
00:17:07 --> 00:17:10
So that's a solvable problem.
297
00:17:10 --> 00:17:12
Well, you say, okay, that was a
little surprising to get an
298
00:17:12 --> 00:17:15
answer for a singular problem.
299
00:17:15 --> 00:17:17
And no, it can happen.
300
00:17:17 --> 00:17:21
If we have a total load
zero it'll happen.
301
00:17:21 --> 00:17:28
But, there is still a but,
that's not the only answer.
302
00:17:28 --> 00:17:31
That picture is a solution.
303
00:17:31 --> 00:17:34
But not the only one.
304
00:17:34 --> 00:17:37
So what my point is going to
be, that when the problem is
305
00:17:37 --> 00:17:41
singular, if there's an
answer, you say great.
306
00:17:41 --> 00:17:44
But then something has to go
wrong and what goes wrong
307
00:17:44 --> 00:17:46
is too many answers.
308
00:17:46 --> 00:17:53
So tell me some more, what
other graphs would draw
309
00:17:53 --> 00:18:00
solutions to this problem.
310
00:18:00 --> 00:18:04
I could shift, I could
lift the whole thing.
311
00:18:04 --> 00:18:07
Here I've got a plus C
that I haven't used.
312
00:18:07 --> 00:18:10
I could just do the
whole thing higher up.
313
00:18:10 --> 00:18:11
Any of these.
314
00:18:11 --> 00:18:17
These would all work.
315
00:18:17 --> 00:18:18
It's like temperature.
316
00:18:18 --> 00:18:23
I don't have an absolute
temperature here.
317
00:18:23 --> 00:18:30
All I've got is, I would have
to, it's not determined because
318
00:18:30 --> 00:18:37
there's a plus C that, the
plus C satisfied everything.
319
00:18:37 --> 00:18:41
A plus C, a constant has zero
slope, it has zero slope, its
320
00:18:41 --> 00:18:42
second derivative is zero.
321
00:18:42 --> 00:18:48
So it's like, unseen
by this equation.
322
00:18:48 --> 00:18:52
And similarly can I just make
the analogy as I always like to
323
00:18:52 --> 00:18:56
do with discrete stuff, so
suppose I, tell me a right-hand
324
00:18:56 --> 00:19:03
side that we think would
probably, is this going to be
325
00:19:03 --> 00:19:05
the same story for this guy?
326
00:19:05 --> 00:19:06
Yes.
327
00:19:06 --> 00:19:11
If I add those, where I
integrated there, here I would
328
00:19:11 --> 00:19:13
add and I get zero, zero, zero.
329
00:19:13 --> 00:19:18
So this has to add to zero
if there's a solution.
330
00:19:18 --> 00:19:22
So let me put for
example, .
331
00:19:22 --> 00:19:26
That would be kind of like our
delta function in one direction
332
00:19:26 --> 00:19:28
and our delta function
in the other.
333
00:19:28 --> 00:19:31
I believe I can
solve that problem.
334
00:19:31 --> 00:19:37
So I'm just carrying, because
I always want you to see the
335
00:19:37 --> 00:19:39
discrete one as well
as the continuous.
336
00:19:39 --> 00:19:43
Continuous involve
this integration.
337
00:19:43 --> 00:19:47
The finite one just
involves adding.
338
00:19:47 --> 00:19:50
The left side adds to zero
so the right-hand side
339
00:19:50 --> 00:19:52
better add to zero.
340
00:19:52 --> 00:19:53
That right-hand side does.
341
00:19:53 --> 00:19:54
Tell me a solution.
342
00:19:54 --> 00:19:57
Well, let me start out
with a seven there.
343
00:19:57 --> 00:20:04
What's the next
guy going to be?
344
00:20:04 --> 00:20:05
See, I want seven.
345
00:20:05 --> 00:20:10
Whatever I put there, I better
have a seven there, right?
346
00:20:10 --> 00:20:12
Seven, seven, good.
347
00:20:12 --> 00:20:16
Minus seven, plus 14, oh geez.
348
00:20:16 --> 00:20:22
I didn't know this
was going to happen.
349
00:20:22 --> 00:20:26
No, I want to get
the answer one.
350
00:20:26 --> 00:20:28
What number goes there?
351
00:20:28 --> 00:20:29
Six, is it six?
352
00:20:29 --> 00:20:31
It's six, yeah, good.
353
00:20:31 --> 00:20:34
Minus seven, 14,
minus six is that.
354
00:20:34 --> 00:20:36
And now my claim is that
we'll come out right
355
00:20:36 --> 00:20:38
on the third equation.
356
00:20:38 --> 00:20:40
So far I've just
matched the first two.
357
00:20:40 --> 00:20:44
Now this one gives minus
seven, plus six, that's
358
00:20:44 --> 00:20:45
minus one, good.
359
00:20:45 --> 00:20:48
So there's a solution.
360
00:20:48 --> 00:20:52
And I'll leave this problem
alone if you tell me the
361
00:20:52 --> 00:20:54
rest, other solutions.
362
00:20:54 --> 00:20:59
That was a solution
to a singular problem with a
363
00:20:59 --> 00:21:04
right-hand side that had total
load zero, so it was ok.
364
00:21:04 --> 00:21:08
But now that's a solution,
but there are more.
365
00:21:08 --> 00:21:13
Tell me another one.
366
00:21:13 --> 00:21:15
I can shift it, right?
367
00:21:15 --> 00:21:18
I could make it .
368
00:21:18 --> 00:21:21
I could add ten to everything.
369
00:21:21 --> 00:21:21
Right?
370
00:21:21 --> 00:21:24
That's the plus C that
I could do over there.
371
00:21:24 --> 00:21:30
That can't change because
17 - 17 is still zero.
372
00:21:30 --> 00:21:35
-17 + 16 will still be
minus one. all good.
373
00:21:35 --> 00:21:39
So actually that just
like helps our intuition
374
00:21:39 --> 00:21:42
and physically my
intuition is this.
375
00:21:42 --> 00:21:49
That I've got this bar and
nothing's holding it.
376
00:21:49 --> 00:21:57
So if I put a weight on it,
nothing to hold it, it'll just,
377
00:21:57 --> 00:22:00
rigid motion will take it
out of sight, no good.
378
00:22:00 --> 00:22:02
But if I put another
equal weight on it,
379
00:22:02 --> 00:22:03
no it's not a weight.
380
00:22:03 --> 00:22:04
What do I call it?
381
00:22:04 --> 00:22:09
If I lift it at that point,
that's the other delta function
382
00:22:09 --> 00:22:13
that's going the other way,
then it will sit there.
383
00:22:13 --> 00:22:18
But it would still be in
equilibrium if I just
384
00:22:18 --> 00:22:21
moved it up to there
or moved it as I like.
385
00:22:21 --> 00:22:26
I don't know if that is
kind of a dumb picture.
386
00:22:26 --> 00:22:31
But it's saying what
we've said from math.
387
00:22:31 --> 00:22:33
Well, you see where
you're question lead.
388
00:22:33 --> 00:22:44
Yeah, thanks.
389
00:22:44 --> 00:22:49
No, the integral, it was--
Watch what we integrated.
390
00:22:49 --> 00:22:50
We integrated u''.
391
00:22:50 --> 00:22:53
392
00:22:53 --> 00:22:55
So that's not the area.
393
00:22:55 --> 00:22:59
We integrated u'' and got,
it's integral was u'.
394
00:22:59 --> 00:23:03
So that just told us that
a difference in slopes
395
00:23:03 --> 00:23:05
at the ends, yeah.
396
00:23:05 --> 00:23:09
Good, because our intuition
automatically is if we're
397
00:23:09 --> 00:23:11
integrating something,
we're finding an area.
398
00:23:11 --> 00:23:15
But here, if it was u , then
I'd be finding the area
399
00:23:15 --> 00:23:19
under u, but we integrated
the second derivative.
400
00:23:19 --> 00:23:23
Right, good.
401
00:23:23 --> 00:23:24
Now let's change the subject.
402
00:23:24 --> 00:23:33
Yes, please.
403
00:23:33 --> 00:23:34
Yeah, I guess so.
404
00:23:34 --> 00:23:44
I'll try.
405
00:23:44 --> 00:23:45
Let's see.
406
00:23:45 --> 00:23:53
So my discrete equation
was, like -u.
407
00:23:53 --> 00:23:57
Yeah, so let's back
up to the beginning.
408
00:23:57 --> 00:23:59
We've got this minus
sign and we're using
409
00:23:59 --> 00:24:00
a second difference.
410
00:24:00 --> 00:24:03
So second differences
have coefficients one,
411
00:24:03 --> 00:24:06
minus two and one.
412
00:24:06 --> 00:24:09
Now I'm reversing the signs
because of my minus.
413
00:24:09 --> 00:24:13
So I have -u at some point.
414
00:24:13 --> 00:24:17
Let's take that as the
point to the left.
415
00:24:17 --> 00:24:21
Two u's at what I'll think
of as the center point.
416
00:24:22 --> 00:24:29
-u_(i-1) is the load
at that center.
417
00:24:29 --> 00:24:37
That center point is
i times delta x.
418
00:24:37 --> 00:24:38
That's where I
would be looking.
419
00:24:38 --> 00:24:44
So now I'm using subscript.
420
00:24:44 --> 00:24:50
It's a little bit of practice
then to take subscripts, take
421
00:24:50 --> 00:24:54
this way of writing the
equation and convert
422
00:24:54 --> 00:24:57
it to a matrix way.
423
00:24:57 --> 00:25:01
It's usually clearer once
you see it as a matrix.
424
00:25:01 --> 00:25:04
Now this is happening
at all the points.
425
00:25:04 --> 00:25:24
At i=1, let's say, I have
-u_0+2u_1-u_2 is f at,
426
00:25:24 --> 00:25:30
agrees with the load at
the first mesh point.
427
00:25:30 --> 00:25:36
That's the center, the
point h, delta x.
428
00:25:36 --> 00:25:42
And then if I want to back up
further, I would have -u_-1,
429
00:25:42 --> 00:25:49
but that doesn't really
exist, plus 2u_0-u_1 should
430
00:25:49 --> 00:25:55
match the load at zero.
431
00:25:55 --> 00:25:57
And so on forward.
432
00:25:57 --> 00:26:00
But now I want to put in
the boundary condition.
433
00:26:00 --> 00:26:01
That's what you want
me to do, right?
434
00:26:01 --> 00:26:03
Put in this boundary condition.
435
00:26:03 --> 00:26:11
So what am I going to take
as boundary condition?
436
00:26:11 --> 00:26:14
It has to be some
approximation to u'(0)=0.
437
00:26:14 --> 00:26:18
438
00:26:18 --> 00:26:20
Maybe I'm never going
to get to minus one.
439
00:26:20 --> 00:26:33
Maybe I don't need minus one.
440
00:26:33 --> 00:26:38
That's right, yeah, exactly.
441
00:26:38 --> 00:26:41
We did.
442
00:26:41 --> 00:26:42
That's what we knew about it.
443
00:26:42 --> 00:26:45
Sending it forward, we knew
about forward difference,
444
00:26:45 --> 00:26:51
so I chose to do it.
445
00:26:51 --> 00:26:53
But then I think better of it.
446
00:26:53 --> 00:26:57
I chose to do it because it
made the point that we, that at
447
00:26:57 --> 00:27:02
that boundary we were
introducing a higher order
448
00:27:02 --> 00:27:08
error, first order error that's
going to wreck things.
449
00:27:08 --> 00:27:11
I mean, it's going to
spoil the, this is
450
00:27:11 --> 00:27:13
second order accuracy.
451
00:27:13 --> 00:27:17
And, but let me do
that first order.
452
00:27:17 --> 00:27:19
So what shall I take?
453
00:27:19 --> 00:27:23
I'm going to approximate that
by u-- Shall I take this
454
00:27:23 --> 00:27:33
one as I did in class?
455
00:27:33 --> 00:27:35
Yes.
456
00:27:35 --> 00:27:39
Ah, plus one, thanks, plus
one, right, thank you.
457
00:27:39 --> 00:27:42
Thank you, good.
458
00:27:42 --> 00:27:44
Okeydoke.
459
00:27:44 --> 00:27:47
Alright.
460
00:27:47 --> 00:27:50
This is how we got
to that equation.
461
00:27:50 --> 00:27:54
If I now bring in this boundary
condition-- I guess I don't
462
00:27:54 --> 00:27:58
have to, let me take your
eye off of that guy for
463
00:27:58 --> 00:28:02
the moment, I think.
464
00:28:02 --> 00:28:05
We're getting
beautiful music here.
465
00:28:05 --> 00:28:07
Is it coming out
of this box or?
466
00:28:07 --> 00:28:08
No.
467
00:28:08 --> 00:28:18
Anyway. so I'm going to use
this boundary condition to say,
468
00:28:18 --> 00:28:22
well ok, if u_1 is u_0, I'm
going to replace
469
00:28:22 --> 00:28:23
this u_0 by u_1.
470
00:28:23 --> 00:28:26
471
00:28:26 --> 00:28:28
This is the direct way.
472
00:28:28 --> 00:28:33
I replaced that u_0 by u_1
in that first equation.
473
00:28:33 --> 00:28:37
And then what I have is -u_1
and 2u_1, so that's the
474
00:28:37 --> 00:28:39
one and I have the -u_2.
475
00:28:40 --> 00:28:44
So do you see that that
equation, when I put those
476
00:28:44 --> 00:28:54
together into a one, is going
to, if this is u_1, this is
477
00:28:54 --> 00:29:01
u_2, this is u_3 onwards, that
first equation is u_1-u_2
478
00:29:01 --> 00:29:03
and that's what I've got.
479
00:29:03 --> 00:29:05
This is u_1-u_2.
480
00:29:05 --> 00:29:09
481
00:29:09 --> 00:29:10
So I did it.
482
00:29:10 --> 00:29:12
I got to that matrix.
483
00:29:12 --> 00:29:15
The matrix is actually
quite an important matrix.
484
00:29:15 --> 00:29:20
But from the point of view
of accuracy in solving this
485
00:29:20 --> 00:29:24
differential equation,
it's not the greatest.
486
00:29:24 --> 00:29:27
It's lost accuracy
at that point.
487
00:29:27 --> 00:29:31
But the way to recover it
turned out to be just a small
488
00:29:31 --> 00:29:35
adjustment at the boundary,
so not a problem.
489
00:29:35 --> 00:29:35
Thanks.
490
00:29:35 --> 00:29:36
That's good.
491
00:29:36 --> 00:29:41
Yes, thanks.
492
00:29:41 --> 00:29:49
Sorry?
493
00:29:49 --> 00:29:49
When the boundary-- sorry.
494
00:29:49 --> 00:29:55
Two boundary conditions
at the same point?
495
00:29:55 --> 00:29:57
That's a good question.
496
00:29:57 --> 00:29:59
So when would we have two?
497
00:29:59 --> 00:30:02
So instead of a boundary
condition at zero and a
498
00:30:02 --> 00:30:05
boundary condition at one,
you're putting them,
499
00:30:05 --> 00:30:06
is that what you mean?
500
00:30:06 --> 00:30:08
Put both boundary
conditions at the end.
501
00:30:08 --> 00:30:10
Ok.
502
00:30:10 --> 00:30:14
So that would be, that would
happen, I would think that
503
00:30:14 --> 00:30:19
would be more, it would be very
typical in a, let me see if
504
00:30:19 --> 00:30:22
there's some space here, yeah.
505
00:30:22 --> 00:30:28
That would be very typical
and we will do it,
506
00:30:28 --> 00:30:30
can I change x to t?
507
00:30:30 --> 00:30:38
Because that's what,
if I have some.
508
00:30:38 --> 00:30:39
What does this
problem look like?
509
00:30:39 --> 00:30:43
And u(0)=0 and u'(0)=0.
510
00:30:45 --> 00:30:52
Both at the same, at the start
equals zero or whatever.
511
00:30:52 --> 00:30:56
So what kind of a
problem is that?
512
00:30:56 --> 00:30:59
Now these are, I would
say, initial values.
513
00:30:59 --> 00:31:03
Initial values instead of
boundary values, I now
514
00:31:03 --> 00:31:05
have initial values.
515
00:31:05 --> 00:31:07
And can I solve it?
516
00:31:07 --> 00:31:10
Yes.
517
00:31:10 --> 00:31:11
So I'm starting at time zero.
518
00:31:11 --> 00:31:12
This is t=0.
519
00:31:14 --> 00:31:18
I'm starting at rest.
520
00:31:18 --> 00:31:23
No velocity and actually
no displacement and just
521
00:31:23 --> 00:31:25
going forward in time.
522
00:31:25 --> 00:31:30
So I could solve that
differential equation.
523
00:31:30 --> 00:31:32
I'd be interested in
the corresponding
524
00:31:32 --> 00:31:36
difference equation.
525
00:31:36 --> 00:31:37
All fine.
526
00:31:37 --> 00:31:39
It's a different
category of problem.
527
00:31:39 --> 00:31:49
This is an initial
value problem.
528
00:31:49 --> 00:32:00
It's like tracking some mass
that's, some satellite.
529
00:32:00 --> 00:32:04
So that's what you're doing
in tracking a satellite
530
00:32:04 --> 00:32:09
or a planet or something.
531
00:32:09 --> 00:32:13
Yeah, tracking a planet
or a satellite.
532
00:32:13 --> 00:32:16
You're solving
equations like this.
533
00:32:16 --> 00:32:18
Forward in time.
534
00:32:18 --> 00:32:22
You know the initial
position and you know
535
00:32:22 --> 00:32:24
the forces acting on it.
536
00:32:24 --> 00:32:26
Probably gravity.
537
00:32:26 --> 00:32:28
And you go forward in time.
538
00:32:28 --> 00:32:31
Yes.
539
00:32:31 --> 00:32:33
What would the matrix be?
540
00:32:33 --> 00:32:34
Good question.
541
00:32:34 --> 00:32:41
What would the
matrix look like?
542
00:32:41 --> 00:32:47
So an electrical engineer would
call a problem like this, and
543
00:32:47 --> 00:32:50
the kind of matrix that I'm
going to write down, I think,
544
00:32:50 --> 00:32:53
would be called causal.
545
00:32:53 --> 00:32:57
That word just popped into my
head, so let me mention it.
546
00:32:57 --> 00:33:01
You know, part of science and
engineering, a big part of it
547
00:33:01 --> 00:33:04
is learning language,
learning words.
548
00:33:04 --> 00:33:10
And you have to learn sort of
the math language and the
549
00:33:10 --> 00:33:14
engineering language for
whatever you're focusing on.
550
00:33:14 --> 00:33:19
But it's good to also to
know a few other languages.
551
00:33:19 --> 00:33:23
Electrical engineering
languages of filters and
552
00:33:23 --> 00:33:28
causal and other things that
we'll see are important.
553
00:33:28 --> 00:33:32
What would the
matrix look like?
554
00:33:32 --> 00:33:35
Here's what I think
it would be.
555
00:33:35 --> 00:33:40
I've made this a plus
there just so I'll
556
00:33:40 --> 00:33:42
have to remember that.
557
00:33:42 --> 00:33:46
I think, so I'm looking
at u_0, u_1, no.
558
00:33:46 --> 00:33:49
Well, u_0 I actually know,
so let me start with
559
00:33:49 --> 00:33:50
u_1, u_2, u_3, u_4.
560
00:33:50 --> 00:33:55
561
00:33:55 --> 00:33:59
What would a typical equal sum,
right side, f_1, f_2, f_3, f_4.
562
00:33:59 --> 00:34:06
1, What do you think, what kind
of a matrix am I going to get?
563
00:34:06 --> 00:34:09
Before I put it in there.
564
00:34:09 --> 00:34:11
This is a good question.
565
00:34:11 --> 00:34:14
What's the shape
of this matrix?
566
00:34:14 --> 00:34:19
It's going to be triangular.
567
00:34:19 --> 00:34:22
Instead of being symmetric
it's going to be triangular.
568
00:34:22 --> 00:34:27
I'm going to find, let's see, a
typical value would be, say,
569
00:34:27 --> 00:34:35
u_3 because I've used
a plus sign, oops!
570
00:34:35 --> 00:34:39
I can't make myself
do it right.
571
00:34:39 --> 00:34:44
1, -2, 1.
572
00:34:44 --> 00:34:54
That would say u_3-2u_2+u_1
would be the new force.
573
00:34:54 --> 00:34:56
This is the kind of thing
we're going to get.
574
00:34:56 --> 00:34:59
One, maybe one something.
575
00:34:59 --> 00:35:00
I don't know what this is.
576
00:35:00 --> 00:35:03
This is up in the boundary,
in the initial values.
577
00:35:03 --> 00:35:10
But from now on it'll
be below the diagonal.
578
00:35:10 --> 00:35:15
It'll be 1, -2, 1.
579
00:35:15 --> 00:35:17
Do you see?
580
00:35:17 --> 00:35:20
We're marching.
581
00:35:20 --> 00:35:25
We're marching forward.
582
00:35:25 --> 00:35:28
We start by knowing these
and then the equation
583
00:35:28 --> 00:35:29
tells us the next one.
584
00:35:29 --> 00:35:31
Then the equation tells
us the next one.
585
00:35:31 --> 00:35:34
That's what initial
value problems do.
586
00:35:34 --> 00:35:39
You're told how you begin and
you take a step, you take a
587
00:35:39 --> 00:35:41
step, take a step every time.
588
00:35:41 --> 00:35:47
And the new value just needs
to know the older values.
589
00:35:47 --> 00:35:50
Do you see the big
difference between that
590
00:35:50 --> 00:35:53
and our problems here?
591
00:35:53 --> 00:35:58
Our problem is looking left
and right looking for
592
00:35:58 --> 00:36:00
back and forward.
593
00:36:00 --> 00:36:02
Back for one condition,
forward for another.
594
00:36:02 --> 00:36:07
We start with one, but
we're, it's more of a, it's
595
00:36:07 --> 00:36:10
like a hitting problem.
596
00:36:10 --> 00:36:15
We start forward, marching
forward in our problems,
597
00:36:15 --> 00:36:19
but we have to hit the
other end correctly.
598
00:36:19 --> 00:36:22
We don't know the slope, we
don't know the starting slope,
599
00:36:22 --> 00:36:24
we know what we want to hit.
600
00:36:24 --> 00:36:31
Whereas these problems, we're
told how we start and we
601
00:36:31 --> 00:36:34
just follow it in time.
602
00:36:34 --> 00:36:40
So that's the difference here.
603
00:36:40 --> 00:36:49
Yeah, sure, okay.
604
00:36:49 --> 00:36:51
That's true.
605
00:36:51 --> 00:36:54
So this'll be known.
606
00:36:54 --> 00:36:56
Yeah, that'll be known.
607
00:36:56 --> 00:36:58
Yeah. u_1 will also be known.
608
00:36:58 --> 00:37:03
Yeah, and really, maybe I
should have got, let me put
609
00:37:03 --> 00:37:06
even the other known one.
610
00:37:06 --> 00:37:08
So we know this, we know this.
611
00:37:08 --> 00:37:12
So those are sort of not in
our, yeah, that shouldn't
612
00:37:12 --> 00:37:23
be in our problem somehow.
613
00:37:23 --> 00:37:28
No, I think, what would
we get in the end?
614
00:37:28 --> 00:37:28
You're always
looking backwards.
615
00:37:28 --> 00:37:29
That's the point.
616
00:37:29 --> 00:37:33
Lower triangular matrices are
always looking, they only look
617
00:37:33 --> 00:37:35
backwards for earlier values
and then they give you
618
00:37:35 --> 00:37:37
the current value.
619
00:37:37 --> 00:37:41
So that's why lower triangular
matrices are so easy to invert.
620
00:37:41 --> 00:37:42
No problem.
621
00:37:42 --> 00:37:46
If it's lower triangular, you
just, like, march forward.
622
00:37:46 --> 00:37:50
And if it's upper triangular,
which way do you march?
623
00:37:50 --> 00:37:54
So if you have an upper
triangular problem, suppose I
624
00:37:54 --> 00:37:59
gave you the problem, let me
make it upper triangular.
625
00:37:59 --> 00:37:59
So x+y+z=7.
626
00:37:59 --> 00:38:03
627
00:38:03 --> 00:38:08
2y+3z=12 and z=17.
628
00:38:08 --> 00:38:11
629
00:38:11 --> 00:38:13
So that's upper triangular.
630
00:38:13 --> 00:38:17
Where do we start in
solving that one?
631
00:38:17 --> 00:38:18
From the bottom.
632
00:38:18 --> 00:38:20
From the right-hand
end, the bottom.
633
00:38:20 --> 00:38:25
And we march backwards in time.
634
00:38:25 --> 00:38:29
And what I was saying about
A, well L times U, yeah,
635
00:38:29 --> 00:38:31
this is worth seeing.
636
00:38:31 --> 00:38:38
What I was saying about A=LU,
it was, you remember that?
637
00:38:38 --> 00:38:40
Those letters?
638
00:38:40 --> 00:38:45
What that was saying was that
this matrix that's looking both
639
00:38:45 --> 00:38:52
ways can be written as a
product of a matrix L that
640
00:38:52 --> 00:38:59
looks behind for old values and
you can go forward with it.
641
00:38:59 --> 00:39:05
And a matrix U, like this one,
this upper triangular, 1, 1, 1,
642
00:39:05 --> 00:39:10
zeroes below that diagonal,
that you go backward with.
643
00:39:10 --> 00:39:12
Somehow that's appealing.
644
00:39:12 --> 00:39:19
That's like aesthetic to break
up a two-way problem into a
645
00:39:19 --> 00:39:24
problem like marches one
way and then the other.
646
00:39:24 --> 00:39:29
And of course, that's what
elimination aims for, is this
647
00:39:29 --> 00:39:33
problem that it can solve by,
the words would be
648
00:39:33 --> 00:39:35
back substitution.
649
00:39:35 --> 00:39:37
When you've started with your
original problem, got to this
650
00:39:37 --> 00:39:44
one, then you just have a, back
substitution, you go backwards.
651
00:39:44 --> 00:39:49
Oh, so much, I'll mention
the Kalman filter.
652
00:39:49 --> 00:39:53
That's a similar process
of going forward, that's
653
00:39:53 --> 00:39:55
called prediction.
654
00:39:55 --> 00:39:57
Going backward, that's
called smoothing.
655
00:39:57 --> 00:40:04
And so, Kalman had the great
idea that he could break these
656
00:40:04 --> 00:40:14
problems that were fundamental
in space computations for
657
00:40:14 --> 00:40:19
prediction and smoothing.
658
00:40:19 --> 00:40:20
Once again, we've got off.
659
00:40:20 --> 00:40:25
Yes?
660
00:40:25 --> 00:40:28
Oh, the beam.
661
00:40:28 --> 00:40:33
Let me help you even more
before the question.
662
00:40:33 --> 00:40:39
I said it's better to
draw the beam this way.
663
00:40:39 --> 00:40:41
I like the beam
better this way.
664
00:40:41 --> 00:40:46
Because the point of the beam
problem is loads are acting,
665
00:40:46 --> 00:40:51
and we'll see this, of course
later, loads are acting
666
00:40:51 --> 00:40:54
perpendicular to the
direction of the beam.
667
00:40:54 --> 00:40:57
That's why the beam bends.
668
00:40:57 --> 00:41:00
So it'll bend a little, right?
669
00:41:00 --> 00:41:04
And that is what leads
us, it's bending moments
670
00:41:04 --> 00:41:05
and other stuff.
671
00:41:05 --> 00:41:10
If you haven't met beams, well,
it'll be great to just have a
672
00:41:10 --> 00:41:15
very, half a lecture about, or
maybe a lecture about beams.
673
00:41:15 --> 00:41:20
That gives a fourth order
equation that I'll
674
00:41:20 --> 00:41:21
write down again.
675
00:41:21 --> 00:41:24
Fourth derivative
equal the load.
676
00:41:24 --> 00:41:39
Now, ready.
677
00:41:39 --> 00:41:42
Yeah, now here I don't
have the negative sign.
678
00:41:42 --> 00:41:47
Because once I've got second
derivatives twice, so the
679
00:41:47 --> 00:41:52
second derivative is,
in some way, negative.
680
00:41:52 --> 00:41:55
I'll complete that
sentence in a second.
681
00:41:55 --> 00:41:59
Somehow the second derivative,
which is the guy that has the
682
00:41:59 --> 00:42:04
1, -2, 1, somehow that's
a negative thing.
683
00:42:04 --> 00:42:07
But fourth derivative is
second derivative of
684
00:42:07 --> 00:42:08
the second derivative.
685
00:42:08 --> 00:42:12
Yeah, do you want to tell me
what the numbers would be?
686
00:42:12 --> 00:42:17
As long as we're wildly
looking forward to fourth
687
00:42:17 --> 00:42:19
derivatives, just, it helps.
688
00:42:19 --> 00:42:28
Do you want to guess what will
a typical row of the matrix B
689
00:42:28 --> 00:42:30
when I go to finite
differences, fourth
690
00:42:30 --> 00:42:32
differences?
691
00:42:32 --> 00:42:36
Probably you've never seen
a fourth difference.
692
00:42:36 --> 00:42:38
You may not have seen
second differences before.
693
00:42:38 --> 00:42:43
That was a big deal, then, to
introduce second differences.
694
00:42:43 --> 00:42:46
Those 1, -2, 1's.
695
00:42:46 --> 00:42:48
That was second differences.
696
00:42:48 --> 00:42:50
Fourth?
697
00:42:50 --> 00:42:53
Yeah, 1, 4, 6, 4, 1
with minus sign.
698
00:42:53 --> 00:42:58
1, -4, 6, -4, and 1.
699
00:42:58 --> 00:43:06
In some way, I would get
that by squaring this guy.
700
00:43:06 --> 00:43:17
So that would be a
fourth difference.
701
00:43:17 --> 00:43:19
Oh, what's the deal with
boundary conditions?
702
00:43:19 --> 00:43:25
What are you figuring on beams,
beam problems for a fourth
703
00:43:25 --> 00:43:30
order equation and a matrix
that's stretching out further.
704
00:43:30 --> 00:43:35
What's going to happen at
the left-hand boundary?
705
00:43:35 --> 00:43:39
I guess my specific question
is, How many boundary
706
00:43:39 --> 00:43:41
conditions do I now need?
707
00:43:41 --> 00:43:42
Four.
708
00:43:42 --> 00:43:44
And the typical is
two at each end.
709
00:43:44 --> 00:43:46
That's the balanced way.
710
00:43:46 --> 00:43:50
That's the way that would make
this matrix sort of symmetric.
711
00:43:50 --> 00:43:57
So I have maybe at this end
I say it's held at zero and
712
00:43:57 --> 00:44:01
maybe it's just sitting
on a log there.
713
00:44:01 --> 00:44:02
Right?
714
00:44:02 --> 00:44:06
That boundary condition I
would call simply supported.
715
00:44:06 --> 00:44:09
That boundary condition
says that u(0)=0.
716
00:44:11 --> 00:44:13
Because it's sitting there.
717
00:44:13 --> 00:44:17
And but the slope doesn't
have to be zero.
718
00:44:17 --> 00:44:20
What does have to
be zero there?
719
00:44:20 --> 00:44:23
Yeah, sort of the
bending moment.
720
00:44:23 --> 00:44:27
Nobody's here
twisting it, right?
721
00:44:27 --> 00:44:32
So the other condition in
that picture would be second
722
00:44:32 --> 00:44:36
derivative equal zero.
723
00:44:36 --> 00:44:43
Maybe my point is that now you
see what I said before, that
724
00:44:43 --> 00:44:46
the getting the boundary
conditions into the problem
725
00:44:46 --> 00:44:49
is often the hardest part.
726
00:44:49 --> 00:44:52
Because I have to replace
u(0)=0, that shouldn't
727
00:44:52 --> 00:44:53
be too hard to do.
728
00:44:53 --> 00:44:57
But I have to use this
other condition somehow,
729
00:44:57 --> 00:45:01
it's going to screw up
the 1, -4, 6, -4, 1.
730
00:45:01 --> 00:45:06
I'll have two boundary rows
at the top, two boundary
731
00:45:06 --> 00:45:08
rows at the bottom.
732
00:45:08 --> 00:45:11
I don't want to go
further today.
733
00:45:11 --> 00:45:15
But I think maybe just
mentioning this gives you
734
00:45:15 --> 00:45:23
the picture of sort of the
how things fit together.
735
00:45:23 --> 00:45:28
We would still have some nice
constant diagonals in the
736
00:45:28 --> 00:45:33
middle, but now we'll have two
boundary rows at each end.
737
00:45:33 --> 00:45:36
So that's something to come.
738
00:45:36 --> 00:45:44
Yes, now back to reality
which is any questions.
739
00:45:44 --> 00:45:52
Lower triangular guy, yeah.
740
00:45:52 --> 00:45:56
What do I mean by
marching forward?
741
00:45:56 --> 00:46:01
So let's see.
742
00:46:01 --> 00:46:04
I'll replace this.
743
00:46:04 --> 00:46:06
Let's see it better.
744
00:46:06 --> 00:46:11
I would replace this by maybe
u, I'll use a different letter,
745
00:46:11 --> 00:46:26
n+1 at u_(n+1)-2u_n+u(n-1) is
some right-hand side if there's
746
00:46:26 --> 00:46:28
a force acting on my thing.
747
00:46:28 --> 00:46:32
So f_n maybe.
748
00:46:32 --> 00:46:37
By marching forward, I just
mean that this equation,
749
00:46:37 --> 00:46:40
that I can go in order.
750
00:46:40 --> 00:46:42
I can start with u_0 and u_1.
751
00:46:43 --> 00:46:47
They come from the
boundary conditions.
752
00:46:47 --> 00:46:49
Then this equation
will tell me u_2.
753
00:46:51 --> 00:46:53
I use the equation.
754
00:46:53 --> 00:46:54
With n as one.
755
00:46:54 --> 00:47:01
This says u_2, some u_1's, some
u_0's, f_1's, all that I know.
756
00:47:01 --> 00:47:07
In other words, once I get
started, I'm on a roll.
757
00:47:07 --> 00:47:10
If I have two boundary
conditions to get me started,
758
00:47:10 --> 00:47:13
then the equation tells me u_2.
759
00:47:14 --> 00:47:16
And then the next
time, u_3-2u_2+u_1.
760
00:47:19 --> 00:47:20
I can find u_3.
761
00:47:21 --> 00:47:24
So I can get those,
I can go forever.
762
00:47:24 --> 00:47:28
If you give me enough to start
on, two things to start,
763
00:47:28 --> 00:47:32
then I march forward.
764
00:47:32 --> 00:47:37
Whereas in our problems, we've
only got one thing to start on
765
00:47:37 --> 00:47:39
and we've got one goal to hit.
766
00:47:39 --> 00:47:44
And that's why we have to solve
the whole system together.
767
00:47:44 --> 00:47:48
This is, we can solve
it step-by-step.
768
00:47:48 --> 00:47:51
This is way faster of course.
769
00:47:51 --> 00:47:57
To be able to just
go forward in time.
770
00:47:57 --> 00:48:01
I'll mention that the topic of
initial value problems and
771
00:48:01 --> 00:48:07
finite differences for them,
we can't get to that.
772
00:48:07 --> 00:48:13
So we're seeing a little bit
here, but it's done properly in
773
00:48:13 --> 00:48:18
18.086 in the second semester
is the initial value
774
00:48:18 --> 00:48:20
problem start part.
775
00:48:20 --> 00:48:27
And that has it's own
interesting questions.
776
00:48:27 --> 00:48:33
Somehow we've talked about
fourth order equations,
777
00:48:33 --> 00:48:39
initial value problems.
778
00:48:39 --> 00:48:42
But no homework problems.
779
00:48:42 --> 00:48:46
So I'm ready for,
or even related.
780
00:48:46 --> 00:48:51
But that's fine with me.
781
00:48:51 --> 00:48:53
Is there a question?
782
00:48:53 --> 00:48:54
Yeah, thanks.
783
00:48:54 --> 00:48:56
Or it doesn't have to be
a homework question,
784
00:48:56 --> 00:49:05
another question.
785
00:49:05 --> 00:49:09
Oh, good question.
786
00:49:09 --> 00:49:11
You mean I should just
send the homework out to
787
00:49:11 --> 00:49:13
Natick where MATLAB is.
788
00:49:13 --> 00:49:16
Do you know that MATLAB
is just 15 miles away?
789
00:49:16 --> 00:49:22
I almost get there, I live
2/3 of the way there.
790
00:49:22 --> 00:49:24
Yeah, so we could just
send the whole thing out
791
00:49:24 --> 00:49:27
there and get it back.
792
00:49:27 --> 00:49:36
That would save a lot of work.
793
00:49:36 --> 00:49:38
I suppose, I'm ok.
794
00:49:38 --> 00:49:40
Why should I say no?
795
00:49:40 --> 00:49:42
Anything MATLAB can do
and you can make it
796
00:49:42 --> 00:49:45
do, I'm ok with that.
797
00:49:45 --> 00:49:48
I don't see that you have
to do things by hand if
798
00:49:48 --> 00:49:50
you've got a better way.
799
00:49:50 --> 00:49:50
That's ok.
800
00:49:50 --> 00:49:53
And then probably the
answer gets printed
801
00:49:53 --> 00:49:55
and you can graph it.
802
00:49:55 --> 00:49:57
So that's fine.
803
00:49:57 --> 00:50:00
So I mean, somehow a
course like this has
804
00:50:00 --> 00:50:03
got two parts to it.
805
00:50:03 --> 00:50:05
Applied math has
two parts to it.
806
00:50:05 --> 00:50:08
The modeling part, set up the
equation, think, what is
807
00:50:08 --> 00:50:10
it you're supposed to do.
808
00:50:10 --> 00:50:13
And then, step two is do it.
809
00:50:13 --> 00:50:15
The numerical part,
the computing part.
810
00:50:15 --> 00:50:19
And that's where MATLAB,
Python, Fortran, whatever,
811
00:50:19 --> 00:50:25
is going to do a lot
of the heavy lifting.
812
00:50:25 --> 00:50:27
Was there another question?
813
00:50:27 --> 00:50:35
So that first homework was
certainly very general
814
00:50:35 --> 00:50:35
intentionally.
815
00:50:35 --> 00:50:40
Because I'm hoping you
will read the book.
816
00:50:40 --> 00:50:47
The lecture, you'll be able to
match the lectures with the
817
00:50:47 --> 00:50:51
book even later on when they
separate a little
818
00:50:51 --> 00:50:54
or separate more.
819
00:50:54 --> 00:50:55
You'll see what we're doing.
820
00:50:55 --> 00:50:59
And those, the homework
problems, you should look at
821
00:50:59 --> 00:51:01
some of the others just to see.
822
00:51:01 --> 00:51:02
Do I know how to do that?
823
00:51:02 --> 00:51:05
Right.
824
00:51:05 --> 00:51:08
Let's stop here for
this first review.
825
00:51:08 --> 00:51:10
I'm sure we'll have more,
questions will build up
826
00:51:10 --> 00:51:12
for the second week.
| 677.169 | 1 |
Browse related Subjects
...Read More for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.Read Less
Good Condition. The books text has writing and highlighting. Minor shelf and corner wear to the books cover and corners. Binding is still in good condition. Scuffing and rubbing to the books cover and corners. Stickers on the books spine and back cover. Quantity Available: 1. Shipped Weight: Under 1 kilo. Category: Mathematics; Calculus; ISBN: 0618547193. ISBN/EAN: 9780618547197. Inventory No: 1561013572
| 677.169 | 1 |
Algorithms and Ice Cream for All
Where shall we locate ice cream stands in our town so that no one has to
travel too far to buy a treat? The problem-solving strategies for this
problem apply to many other situations that require planning for
facilities. Students will have a chance to grapple with the notion of
proof and decide what makes a solution satisfactory. They are also exposed
to an important unsolved problem in mathematics.
| 677.169 | 1 |
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Mathematical programming studyLINK (Service en ligneINK (SpringerÉtats-Unis programming society (Stati Uniti d' America TheVoorburg, Países Bajos Society (Amsterdamüísticaàticaáticasatisk optimization programming studyymalizacja matematycznaprogrammation mathématique périodiqueProgrammation (Mathématiquesazione matematicaming (Mathematics)owanie matematyczne
| 677.169 | 1 |
Click on this books subject categories to see related titles:
Written by authorities in Mathematics, Algebra 1 (California Edition) by Stanley A. Smith provides an excellent foundation for Mathematics studies. Stanley A. Smith's style is excellently suited towards Mathematics studies, and will teach students the material clearly without overcomplicating the subject. This revision raises the bar for Algebra 1 (California Edition)'s high standard of excellence, making sure that it stays one of the foremost Mathematics studies textbooks.
Customer Book Reviews
Fabulous Algebra 1 book for students, teachers, and tutors
By Tinamon Mar 20, 2009
First off, I am a tutor to many Algebra 1 students, including some who take algebra with me for h.s. credit in lieu of taking it at school. I am very familiar w/myriad algebra texts.
This book is a jazzier version of the 1994 publishing by Stanley Smith under the Addison Wesley label (owned by the same publishing house as Prentice Hall). I wrote in my review of the 1994 book that my only suggestion would be to take out Chapters 14 & 15 on probability and trig, as they don't really belong in an Alg 1 book. Coincidentally, this book has done exactly that. Hooray!
The font, colors, typography, and imagery are more eye-catching than the bland 1994 book, and there are fewer problems of the purely "drill, drill" variety. They've replaced some of those problems with more challenging application problems toward the end of each assignment, but there are still sufficient problems for assigning many practice & drill problems. In fact, most of the problems are exactly the same as in the 1994 text.
Overall, it's a nice improvement over the older text. They made it more visually and otherwise interesting *without* sacrificing content, as so many algebra texts do. This alone sets it apart from the majority of US-published algebra texts out there. (I tend to agree with a former teacher of mine when he said that, in his experience, the quality of a text is inversely proportional to the number of pretty pictures in it.) :-)
I will continue to refer my students to algebra texts authored by Stanley Smith.
high school algebra
By E. Riveraon Jan 20, 2012
Great book to review or improve algebra for high school. Covers all important concepts. Great for anyone having trouble learning the basics.
great explanations
By Javier Floreson Aug 03, 2013
Bought it for my younger brother to get a head start In the summer. May be an old version but it provides a great foundation.
Math anyone?
By Mohoganyon Mar 29, 2014
Serves it purpose as a replacement to my son's lost algebra book. Used book arrived as described and pretty fast.
Algebra 1 Received
By Trishon Jan 11, 2014
I bought this for a 70+ friend and hope to borrow it from him at some point - love algebra and looking forward to a little review
Used and in perfect condition!
By Deerockloveon Sep 30, 2012
I am very satisfied! Book is in great condition! Love it, it has helped me review for a big test. Very helpful
Teachers can afford to buy books for students
By Donna J. Maddenon Jun 26, 2011
This book was in perfect condition. I was able to buy it for a student that didn't have an Algebra book. It arrived very quickly, and his mom (not so much the student) was thrilled.
Tutor Review: Perfect for students, parents & tutors
By Desijatton Nov 01, 2013
Prentice Hall has done a great job at presenting Algebra 1 to middle schoolers in this book. It is an easy to read and use as a guide for all of my students. Great book to improve and be ready for high school math. Great for anyone having trouble learning the basics, and a great addition for concept review for tutors.
algebra 1 text
By Dana L. Adamsonon Feb 12, 2013
This was a great purchase for the quality and the price. I would definately recommend this item to anyone to buy.
It is what it is.
By Eric Watkinson Jun 11, 2013
It is a high school Algebra 1 textbook, that's for sure. It has information, just like I would expect a textbook to have.
Book Summary: The title of this book is Algebra 1 (California Edition) and it was written by Stanley A. Smith. This particular edition is in a Hardcover format. This books publish date is Jun 12, 2001 and it has a suggested retail price of $94.40. It was published by Pearson Prentice Hall and has a total of 704 pages in the book. The 10 digit ISBN is 0130442631 and the 13 digit ISBN is 9780130442635. To buy this book at the lowest price, Click Here.
| 677.169 | 1 |
About this courseEntry requirements
English reading and writing skills, and maths to at least GCSE grade C or equivalent are required. You will need to have general skills and knowledge base associated with a GCSE course or equivalent standard.
This specification is designed to:
develop the student's understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
develop abilities to reason logically and to recognise incorrect reasoning, to generalise and to construct mathematical proofs
extend their range of mathematical skills and techniques and use them in more difficult unstructured problems
use mathematics as an effective means of communication
acquire the skills needed to use technology such as calculators and computers effectively, to recognise when such use may be inappropriate and to be aware of limitations
develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
On this course you will study six units:
AS Level
Unit 1 MPC1 Core 1
Unit 2 MPC2 Core 2
Unit 3 MS1B Statistics 1B
A2 Level
Unit 4 MPC3 Core 3
Unit 5 MPC4 Core 4
Unit 6 MS2B Statistics 2
Each unit has 1 written paper of 1 hour 30 minutes.
Course Content
AS Level
Unit 1 MPC1 Core 1
Co-ordinate Geometry
Quadratic functions
Differentiation
Integration
Unit 2 MPC2 Core 2
Algebra and Functions
Sequences and Series
Trigonometry
Exponentials and logarithms
Differentiation
Integration
Unit 3 MS1B Statistics 1B
Statistical Measures
Probability
Discrete Random Variables
Normal Distribution
Estimation
A2 Level
Unit 4 MPC3 Core 3
Algebra and Functions
Trigonometry
Exponentials and Logarithms
Differentiation
Integration
Numerical Methods
Unit 5 MPC4 Core 4
Algebra and Functions
Coordinate Geometry in the (x, y) plane
Sequences and Series
Trigonometry
Exponentials and Logarithms
Differentiation and Integration
Vectors
Unit 6 MS2B Statistics 2
Poisson distribution
Continuous random variables
The t-distribution
Hypothesis Testing
Chi-squared tests
AS +A2 = A Level in Maths with Statistics. Both AS and A2 level courses and examinations must be successfully completed to gain a full A Level.
AQA Specification 6360
Paper Based Version
The course comes to you as a paper-based pack delivered by courier
You will be given guidance through the Study Guide on the nuts and bolts of studying and submitting assignments
Postal assignments cannot be accepted without prior permission from the tutor
Online Version
Our online A-Level courses are fully digitised so you can study on any smart device. Your learning programme is completely flexible so you can study at a pace that suits you. All our content is broken down into bite size chunks to make your learning more manageable and effective.
Your course of study is broken down into units and sections, each of which contains lessons, activities and test papers.
Courses are delivered on our Moodle based Digital Learning Environment CloudPort allowing you to study from anywhere on any smart device as long as you have access to the Internet.
The course concludes by preparing you for examination using past papers in your chosen subject.
The course contains a number of assignments which your tutor will mark and give you valuable feedback on. We call these Tutor Marked Assignments (TMAs). You need only send the TMAs to your tutor for comment, not the self-assessment exercises which are also part of the course to help you gauge your progress.
Exams are taken at an AQA centre and we can provide an extensive list of centres for you. Please read our FAQs for further information
Our A Levels come with tutor support for 24 months.
You will have access to a tutor, via email, who will mark your work and guide you through the course to help you be ready for your examinations. In addition you will be supplied with a comprehensive Study Guide which will help you through the study and assessment process.
If you are interested in learning more about business structures in the contemporary marketplace, then this home study course is the ideal way to develop your knowledge. Through this distance learning course, you will gain an overview of modern business models, major topical issues and stakeholder perspectives and learn how to evaluate both the internal structures and the dynamic external environment operating on a business.
From planning and financing a small business, to human resources and management issues, this A-Level course for home study offers you a comprehensive overview of business models. So whether you are seeking an A-Level qualification to prepare you to study business at a higher level, or whether you are keen to develop your knowledge of business more generally, then this A-Level course includes the knowledge you need to gain an edge on the competition.As green issues continue to gain in importance, now is the perfect time to learn more about the environment with this compelling home study course from UK Distance Learning & Publishing. Based on the AQA Environmental Studies A-Level specification, this distance learning course covers such key topics as: the living environment; the physical environment; energy resources and environmental pollution; and biological resources and sustainability.
This home study course is ideal for students wishing to study Environmental Studies at a higher level, or for those seeking careers in ecology, conservation or marine biology. It is also relevant to those studying for general interest. As we all become increasingly aware of the impact we have on the Earth, this distance learning A-Level course will help you to learn more about the fascinating issues involved in the preservation of our planet.
Through UK Distance Learning & Publishing, the fascinating subject of A-Level Biology is now available to distance learning students for study at home. Closely based on the AQA A-Level Biology specification, this comprehensive course will take you through the core topics of biological study, allowing you to gain the thorough grounding needed to prepare you for A-Level examination or to study at a higher level.
This home study course provides the opportunity for varied and in-depth study, including the topics of: Biology and Disease; The Variety of Living Organisms; Populations and Environment; and Control in Cells and in Organisms. The course also includes information on the practical skills that you will need for your assessment.
This distance learning course in A-Level English Language and Literature is based on the AQA English Language and Literature A specification and treats English Language and Literature as a combined discipline. In this home study course, students will study four units. These are: Integrated Analysis and Text Production; Analysing Speech and Its Representation; Comparative Analysis and Text Adaptation; and Comparative Analysis through Independent Study. This course allows students to study non-fiction writing as part of their A-Level studies and to choose from a list of set texts in order to prepare individual coursework on a theme of their choice.
Prepared by expert tutors at UK Distance Learning and Publishing, this home study course is suitable for those with a general interest in English literature and language or for those who wish to progress to the study of English language and literature at university level. Interested students should already possess a GCSE in English, or an equivalent qualification.
| 677.169 | 1 |
92.210 Functions and Modeling
Functions and Modeling
Course Details
Min Credits
3
Max Credits
3
Course ID
37657
Status
Active
Engage in lab-based activities designed to strengthen their problem-solving skills and expand knowledge of the topics in secondary mathematics, focusing especially on topics from precalculus and the transition to calculus. Explore a variety of contexts that can be modeled using families of functions. Topics include conic sections, parametric equations and polar equations. Multiple representations, transformations, data analysis techniques and interconnections among geometry, probability and algebra. Quantitative approaches and building relationships between discrete and continuous reasoning will be recurrent themes.
| 677.169 | 1 |
This is a free, online textbook that is offered by the author. It is meant to cover exactly what the title says, and...
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This is a free, online textbook that is offered by the author. It is meant to cover exactly what the title says, and includes information on:Linear algebra, determinants, Gaussian elimination, LU, Cholesky;Affine geometry;Polynomials, PID's, UFD's; andBasic Topology, differential calculus of Algebra and Analysis for Computer Science to your Bookmark Collection or Course ePortfolio
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Select this link to open drop down to add material Basics of Algebra and Analysis for Computer Science'Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of...
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'Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. This text includes many detailed examples for each section along with several problems for students to practice and master concepts. Complete answers are included for students to check work and receive immediate feedback on their progress. Topics covered include: pre-algebra review, solving linear equations, graphing linear equations, inequalities, systems of linear equations, polynomials, factoring, rational expressions and equations, radicals, quadratics, and functions including exponential, logarithmic and trigonometric. Each lesson also includes a World View Note which describes how the lesson fits into math history and into the world, including China, Russia, Central America, Persia, Ancient Babylon (present day Iraq) and more and Elementary Algebra to your Bookmark Collection or Course ePortfolio
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This is a free online textbook offered by BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is...
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This is a free online textbook offered by into math to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Blast into math
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This free online textbook 'is suitable for both students and a general audience interested in learning what pure mathematics...
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This free online textbook 'is will to your Bookmark Collection or Course ePortfolio
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This is a free textbook from BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for...
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According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is...
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According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.Although this book may be more meaningful to the student who has had some calculus, there is no prerequisite other than a measure of mathematical maturity. The text is an expansion and refinement of the author's lecture notes developed over ten years of teaching proof courses at Virginia Commonwealth University. The text is catered to the program at VCU to an extent, but the author kept the larger audience of undergraduate mathematics students of Proof to your Bookmark Collection or Course ePortfolio
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Select this link to open drop down to add material Book of Proof is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This...
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This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as several othersculus
The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the...
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The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to
| 677.169 | 1 |
Mathematical equations
This is a discussion on Mathematical equations within the Game Programming forums, part of the General Programming Boards category; I was wondering if any of you have a link, or list of all the different mathematical equations for figuring ...
Mathematical equations
I was wondering if any of you have a link, or list of all the different mathematical equations for figuring out stuff like cross products of vectors, matrical algebra,etc. its getting tiresome sometimes wading through thousands of webpages to find the equation I need, and I dont have many textbooks lying around here.
Seriously, this is the best ever. It gets right down to writing proofs of all of the most complicated mathematical equations. It's difficult to understand everything 100% unless you are in college classes, but I'm still in high school and have gotten a LOT of use out of it (I still don't understand absolutely everything in the book though)
is there any book that can get someone taking Algebra I to learn Matrix and Vector math? Everything I've seen assumes you are in high-level math. Or is there a book you can recommend that can bring my skills up to where they need to be to learn Vector and Matrix math stuff?
Frenchfry164 - Vectors aren't that tough. You might have to learn some things if you are in Algebra I before you can understand them, but so much the better. You'll just be the math whiz in your grade. If you read a little bit about what vectors are from a geometry or algebra site and then read a couple tutorials on applying them to 3D (or 2D) then you shouldn't have too much trouble. However, if you don't know trig, learn it before you try vectors, it's definitely a prerequisite. Luckily, trig isn't hard either.
to Silvercord: thanks for the book suggestion, I ordered it, and recieved it yesterday, and it is really really nice. I just need to get up to nack on my calculus(im 16, in my 2nd year of highschool, and havent started any yet).
P.S. I am homeschooled, which is kind of fun, as I can just go, "Hey, I need some calculus, can you order me some textbooks", and get them.
That's pretty cool Blade. Seeing as how I have the book too you can ask me questions(if needed). My math knowledge probably isn't above and beyond yours, but I've had the book longer . As you can see the book is pretty complicated. I personally don't expect a complete understanding of the material for a couple of years (i.e being able to write proofs).
I have gotten a lot of use out of it already in my little computer game.
| 677.169 | 1 |
0321620917
9780321620910
Details about Intermediate Algebra for College Students:
The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process.
| 677.169 | 1 |
College and Career Readiness
MATH 131: Explorations in Mathematics
MATH 131: Explorations in Mathematics
Prerequisite: -Completion of MATH 093 OR
-Placement at college level math
This course focuses on mathematical reasoning and the solving of real-life problems, rather than on routine skills and appreciation. Three or four topics are studied in depth, with at least three chosen from the following list: counting techniques and probability, graph theory, logic/set theory, mathematical modeling, mathematics of finance, game theory, linear programming, and statistics. A scientific or graphic calculator are required for this course. 3 credit hours IAI GEC Code - M1 904
| 677.169 | 1 |
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If you need help - Hop on the "COOL BUS" with me. I'll take you on a journey that you'll never forget!
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The best thing that I've found about the creation of Algebra-class.com is that I've been able to help thousands of people from all over the world and from different walks of life. Each one of you may have different needs, so to help you get the most from Algebra-class.com, I've created a special page for each of you. Click on the icon that best describes YOU for a list of resources that will enhance your learning of Algebra.
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Education has introduced ALEKS 360, a mathematics solution that combines an artificial intelligence and personalized learning program with a fully integrated, interactive e-book package. ALEKS 360 delivers assessments of students' math knowledge, guiding them in the selection of appropriate new study material, and recording their progress toward mastery of course goals. Through adaptive questioning, ALEKS accurately assesses a student's knowledge state and delivers targeted instruction on the exact topics a student is most ready to learn.
The e-books featured within ALEKS 360 are interactive versions of their physical counterparts, which offer virtual features such as highlighting and note-taking capabilities, as well as access to multimedia assets such as images, video, and homework exercises. E-books are accessible from ALEKS Student Accounts and the ALEKS Instructor Module for convenient, direct access.
The initial e-books to be offered in ALEKS 360 include: Introductory Algebra, Second Edition, by Julie Miller and Molly O'Neill; Intermediate Algebra, Second Edition, by Miller and O'Neill; College Precalculus, Second Edition, by John W. Coburn; and College Algebra, Second Edition, by Coburn.
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Calculation of Drug Dosages dosage calculation work-text helps students master the critical skills necessary to competently and confidently calculate drug dosages. Innovative and practical, it includes information on the ratio and proportion, formula and dimensional analysis methods of drug calculation, and numerous practice problems to accompany these methods. Ideal for students who need an extensive math review in addition to drug calculations content, this new edition features a more logical organization, a new chapter addressing medication administration to critically ill patients, and more practice problems on calculations for pediatric patients. Learning objectives help students focus on key content as they read and study. Chapter worksheets provide students the opportunity to practice solving realistic problems. Posttests help students identify their areas of strengths and weaknesses. Full-color drug labels provide a more realistic representation of medication administration. A comprehensive posttest at the end of the book helps students assess their knowledge of the calculation of drug dosages. A comprehensive glossary defines important terms. A new chapter on Critical Care IV Flow Rates addresses medication administration to critically ill patients. Content has been reorganized to create a more logical flow for learning. Approximately 20 more practice problems have been added on calculations for pediatric patients.
PART I Review of Mathematics
Review of Mathematics Pretest
3
(4)
Fractions
7
(22)
Pretest
7
(2)
Learning Objectives
9
(2)
Changing an Improper Fraction to a Mixed Number
11
(1)
Changing a Mixed Number to an Improper Fraction
11
(1)
Lowest Common Denominator
11
(2)
Changing a Fraction to an Equivalent Fraction with the Lowest Common Denominator
12
(1)
Changing a Mixed Number to an Equivalent Fraction with the Lowest Common Denominator
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More About
This Textbook
Overview
Tailored to mirror the AP Statistics course, The Practice of Statistics became a classroom favorite. This edition incorporates a number of first-time features to help students prepare for the AP exam, plus more simulations and statistical thinking help, and instructions for the TI-89 graphic 3, 2010
AP Statistics Book
Though I haven't started using the textbook at school yet, all I've heard is that it is easily understandable with a comprehensive usage guide for calculators. The book itself was in great condition although I picked one of the lowest price/rank. Thank you!
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Anonymous
Posted February 18, 2006
A must for any high school stat class
This is the best mathmetics textbook I have ever used. The diagrams and definitions are supurb and easy to understand. This book makes statistics come alive for the average student, but it also has great depth for the serious statistican. This really is a great textbbook!
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Reaching Algebra Readiness (RAR): Preparing Middle School Students to Succeed in Algebra - The Gateway to Career Success
Research has shown that algebra is the doorway and gateway for future success of students in many aspects, including high school graduation, attending and success in college, and professional earning power. And the most important key to students' success in algebra is their readiness. This book is not only a program that addresses algebra readiness; it is also a fundamental reform effort, based on the National Mathematics Advisory Panel's (NMAP's) Final Report (spring, 2008). The book approaches mathematic skills deficiencies on an individual basis, much like an IEP addresses the individual needs of a student with disabilities. The Reaching Algebra Readiness (RAR) process consists of four components: (1) Diagnostic, assessing student's mastery of the skills needed to take algebra; (2) Prescriptive, developing an individualized plan to address specific math deficiencies; (3) Intervention, utilizing tools and resources (parental involvement, effective teaching strategies, etc), to improve students' mathematics skills; and (4) Drills and Effective Teachings Strategies, mathematics is a discipline and, simply, there is no way of avoiding practice and drilling in reaching algebra readiness, which can be enhanced significantly by implementing proven effective teaching strategies. The Reaching Algebra Readiness (RAR) process and the related materials presented in this book will be revolutionary in helping all students acquire the math skills needed for success in algebra and beyond. This book is a must-guide for math teachers, parents who home school, parents who are looking for solutions, and educators pursuing fundamental education reforms
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Description revision app teaches you everything you need to know for GCSE Maths. It combines the separate apps for Number, Algebra, Geometry, Measures, Statistics and Probability produced by Haslam and Hall Publishing, a leading educational publisher in the UK.
Features: * Includes Foundation and Higher levels. * Revise the key facts for GCSE Maths. * Take Quick Quizzes and try to beat your saved best score. * OVER 1000 MULTIPLE CHOICE QUESTIONS with full worked solutions. * No internet connection needed once installed. * Suitable for all exam boards (AQA, Edexcel, OCR).
Revision Buddies brings GCSE students a comprehensive Maths revision app, covering the key topics across the higher and lower tiers of the AQA, OCR and Edexcel GCSE exam boards.
Over 1000 questions testing your knowledge, with explanations and progress charts to allow you to monitor your development and grow at your own pace.
Use our app anywhere, any time to get the most out of your revision.
Key features: Option to choose higher or lower tier, calculator or non calculator, based on your level 1000s of multiple choice questions Explanations to further understanding Choose to repeat difficult questions or select new questions at random Share your results with friends on Twitter and Facebook Monitor your progress with performance based graphs Test yourself with direct access to past papers and mark schemes, unique to this app
Whether you're on the bus, waiting at the doctors or chilling on the beach, use our apps to help you ace your exams!
All content has been written to the highest standard by Colin Stobart, since 2008 Colin has been Head of Mathematics at Sherborne International, a part of Sherborne School in Dorset. Prior to this he spent over 20 years at international schools in Malaga, Spain and Kuwait City. Throughout most of this time he has been Head of Department or Head of Secondary/ Assistant Head. Colin is an Assistant Examiner for Cambridge International Examinations marking GCSE/IGCSE and A2 levels each November and June. He is also a published author working with HarperCollins on IGCSE texts. Colin is dedicated to his subject and has striven to ensure that this content is in line with the requirements of the Edexcel, OCR and AQA GCSE exam boards.
Over 250 revision notes and 2700 questions with solutions and explanations on Number, Algebra, Stats, Geometry.
Includes syllabus for Foundation and Higher levels for all exams boards including OCR, EDEXCEL,AQA,WJEC,CCEA etc. A complete GCSE Maths revision app.
• D• PROGR• MOCK TEST
After•Test your knowledge of GCSE Chemistry Full version has 2700 questions across 270 subtopics. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Features include: • HIGHEST QUALITY and QUANTITY Over 2700 questions in all. High quality content written by experienced GCSE tricksTry out this Lite version of CGP's brilliant GCSE Science apps — for free! It's got all the features of the full versions, but it only contains questions for a few topics to give you a taster. Here's what's on offer…
• Tons of multiple-choice questions, with short explanations of each answer • Three game types — Best of 10, Sudden Fail and Time Trial • Q&A cards — test yourself (or a friend) on the important facts • Progress tracking shows you how well you're doing in each module • Page references to CGP's matching Revision Guides for more info on each topic • Coverage of the AQA, Edexcel, OCR Gateway and OCR 21st Century exam boards
If you like this Lite app, there are full versions available for GCSE Core Science, Additional Science, Biology, Chemistry and Physics!
Take a breath and make your GCSE preparation a fun activity with our collection of GCSE apps. Here comes the most comprehensive Algebra 730 questions across 73 subtopics. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
• HIGHEST QUALITY and QUANTITY 730 questions and 73 revision notes in all just for Algebra3D coordinates Parallel and perpendicular lines Gradient-Intercept method Drawing a line with a given gradient Finding the equation of a line from its graph Uses of graphs- finding formulae or rules Significant points of a quadratic graph Cubic graphs Exponential graphs Reciprocal graphs Graphs of loci and trig functions Solving equations by the method of intersection Sine and cosine graphs Transformations of the graph y = f(x)
Developed by Loughborough University, the mathscard GCSE app contains hundreds of examples of maths formulae, graphs and diagrams. The GCSE app is based on the hugely successful Loughborough A-level app and is designed to help students with their exam revision when at home or on the move. Number and Arithmetic, Algebra, Graphs, Statistics and Probability, Geometry and Measurement and much more are all covered in this handy resource.
LearnersCloud revision videos for GCSE Maths make it easy to learn, revise and test yourself on the go.
Each tutor-led video has been specially developed by a fully qualified GCSE Maths teacher to take you through the key topics and techniques, step by step.
Start today and achieve the results you deserve.
Covers all UK leading exam board specifications.
Please note. *These videos are streamed on-demand for immediate viewing and require an internet connection. We recommend using a WI-FI connection to avoid charges incurred as a result of exceeding your data allowance 50 University in
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Taking a Deep Look into 3D Data: Volumetric Rendering and Processing
Markus van Almsick
This video explains the principles of volume rendering and the art of constructing the right transfer functions. Markus van Almsick explores the drawbacks and extravagant possibilities of this new visualization modality and applies it to real-world data.
Channels: Virtual Events
Discover functional programming with Mathematica. In this course from the Wolfram Mathematica Virtual Conference 2011, you'll learn the core constructs, functions, and evaluation rules of a dynamic, functional language. See how to transition your thinking from procedural to ...
Jon McLoone, director of technical communications and strategy at Wolfram Research Europe, discusses new developments based on the Wolfram Language, including Wolfram Programming Cloud, Mathematica Online, and the ...
Wolfram technologies are the tools for providing interactive and engaging materials for STEM education. In this video, Conrad Wolfram shares examples and explains why Wolfram is uniquely positioned to be ...
In this talk, Etienne presents the new machine learning functionalities of the Wolfram Language (Classify, Predict, and related functions). These functionalities aim to simplify the practice of machine learning by ...
Mathematica provides many approaches to producing dynamic visualizations. This talk uses a number of examples to illustrate the principles involved in constructing graphics sequences, manipulating simulated cameras, building ...
This Wolfram Mathematica Virtual Conference 2011 course gives educators an overall picture of how Mathematica can benefit an engineering curriculum with examples of modeling, simulation, visualization, and ...
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9780471669609 edition with a publication date of 12/1Elementary Linear Algebra
Elementary Linear Algebra, 10th Edition
Summary
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. Clear, accessible, step-by-step explanations make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.
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This site from Northern Illinois University provides online notes for students using the Abstract Algebra textbook (which is also available online). The materials cover the topics of integers, functions, groups,...
This site includes materials on a variety of topics relating to general number theory. Each link provides a short example that would provide helpful supplemental materials in mathematics education. The lessons vary from...
This series of lectures, created by Salman Khan of the Khan Academy, features topics covered in the first two or three semesters of college calculus; Everything from limits to derivatives to integrals to vector...
This series of videos, authored by Salman Khan of the Khan Academy, features non-trigonometry pre-calculus topics. A solid understanding of all of the topics in the "Algebra" playlist should make this playlist pretty...
This learning object from Wisc-Online covers the square, examining the properties and components of the shape. The lesson uses the geometric formulas for finding the perimeter and area of the shape. Practice questions...
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History of Mathematics : An Introduction - 2nd edition
add addAncient Mathematics The Beginnings of Mathematics in Greece Archimedes and Apollonius Mathematical Methods in Hellenistic Times The Final Chapters of Greek Mathematics
PART II: MEDIEVAL MATHEMATICS: 500-1400
Medieval China and India The Mathematics of Islam Mathematics in Medieval Europe Mathematics Around the World
PART III: EARLY MODERN MATHEMATICS: 1400-1700
Algebra in the Renaissance Mathematical Methods in the Renaissance Geometry, Algebra, and Probability in the Seventeenth Century The Beginnings of Calculus
PART IV: MODERN MATHEMATICS: 1700-2000
Analysis in the Eighteenth Century Probability, Algebra, and Geometry in the Eighteenth Century Algebra in the Nineteenth Century Analysis in the Nineteenth Century Geometry in the Nineteenth Century Aspects of the Twentieth Century
Answers to Selected Problems General References in the History of Mathematics Index and Pronunciation Guide06 +$3.99 s/h
Acceptable
GreenEarthBooks Portland, OR
Help save a tree. Buy all your used books from Green Earth Books. Read. Recycle and Reuse.
$1922 +$3.99 s/h
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Kings Ridge Media WI Appleton, WI
1998-0365.06 +$3.99 s/h
Acceptable
Anybook Ltd. Lincoln,
1998 This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In fair condition, suitable as a study copy. No dust jacket., 1500grams, ISBN...show more: 0321016181
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HOW UDEMY WORKS?
COURSE DESCRIPTION
Videos on pre-algebra. You should be ready for the Algebra playlist if you understand everything here.
What am I going to get from this course?
Over 23 lectures and 3.5 hoursAdding/Subtracting negative numbers
09:15
Adding and subtracting negative numbers
2
Multiplying and dividing negative numbers
08:28
Multiplying and dividing negative numbers
3
Adding and subtracting fractions
09:48
How to add and subtract fractions.
4
Multiplying fractions
08:25
Multiplying fractions
5
Dividing fractions
08:58
Dividing fractions
6
Introduction to Order of Operations
09:40
Order of Operations
7
More Complicated Order of Operations Example
05:20
More Complicated Order of Operations Example
8
Level 1 Exponents
09:45
Basic Exponents
9
Level 2 Exponents
06:25
negative exponents
10
Level 3 exponents
09:11
fractional exponents
11
Negative Exponent Intuition
04:38
Intuition on why a^-b = 1/(a^b) (and why a^0 =1)
12
Exponent Rules Part 1
09:43
Introduction to exponent rules
13
Exponent Rules Part 2
07:43
2 more exponent rules with an introduction to composite problems
14
Simplifying radicals
09:43
Using exponent rules to simplify radicals or square roots
15
Introduction to Logarithms
09:47
An introduction to logarithms
16
Unit conversion
09:16
Metric unit conversion
17
Speed translation
09:55
Translating speed units
18
Introduction to logarithm properties
09:14
Introduction to the first two logarithm properties.
19
Introduction to logarithm properties (part 2)
10:04
Second part of the introduction to logarithm properties.
20
Scientific Notation
20:48
Introduction to Scientific Notation
21
Scientific Notation Examples
12:49
More scientific notation examples
22
Introduction to Ratios (new HD version)
14:13
What a ratio is. Simple ratio problems.
23
Unit Conversion Example: Drug Dosage
10:44
Unit Conversion Example: Drug DosagePre-algebra
3
0
0
0
1
AVERAGE RATING
NUMBER OF RATINGS
4
REVIEWS
Brian Marcin
2 years ago
Sal Rules!
This was a great course, I used it to refresh myself for a college placement test. Sal gives the lectures and examples in a way that doesn't make it boring or monotonous and commits it to memory. I think I will do well, thanks to Sal!
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Worksheets for Classroom or Lab Practice for Elementary Algebra for College Students
Student Solutions Manual for Elementary Algebra for College Students
Elementary Algebra For College Students, 9/e
Summary
This dynamic new edition of this proven series adds cutting edge print and media resources. An emphasis on the practical applications of algebra motivates learners and encourages them to see algebra as an important part of their daily lives. The reader-friendly writing style uses short, clear sentences and easy-to-understand language, and the outstanding pedagogical program makes the material easy to follow and comprehend.KEY TOPICSChapter topics cover real numbers, solving linear equations and inequalities, formulas and applications of algebra, exponents and polynomials, factoring, rational expressions and equations, graphing linear equations, systems of linear equations, roots and radicals, and quadratic equations.For the study of Algebra.
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Linear Algebra: A First Course with Applications
Written for students, this book explores the fundamental ideas of linear algebra. Moving from the specific to the general, the author raises questions, provides motivation, and discusses strategy before presenting answers. Topics covered include vector spaces, subspaces, basis, span, linear independence, eigenvalues, and eigenvectors.
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More About
This Textbook
Overview
This text provides a strong foundation to precalculus that focuses on a small number of key topics thereby emphasising depth of understanding rather than breath of coverage. It provides a solid way to motivate concepts and develop critical thinking skills. The new fourth edition emphasises functions as models of change. It contains superior exercises and applications that motivate the concepts students can use to fully grasp precalculus
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Technology: You will need a graphing calculator
for this course.I strongly recommend
a TI-83, TI-83 Plus or TI-84.We will use
an online system, WeBWorK, for homework assignments. Course
materials will be available on the class website.
Course Description: Inspired by problems in astronomy,
Isaac Newton and Wilhelm GottfriedLeibnitzdeveloped the
ideas of calculus roughly 300 years ago. Since then,
calculus has provided the foundation for advances in many
other fields, even those which seem far removed from
mathematics. You will find applications in chemistry,
physics, economics, biology, medicine, business, psychology,
and of course mathematics. Calculus is so important that it
is often considered the gateway to many of the disciplines
in which it is used.
The power of calculus lies in its
power to reduce complicated problems to simple rules and
procedures. While these procedures can be (and often are)
taught with little regard to the underlying mathematical
concepts or their practical uses, our emphasis will be on
understanding all of these: concepts, procedures and uses.
We will engage in the full mathematics process, which
includes searching for patterns, order and reason; creating
models of real world situations to clarify and predict
better what happens around us; understanding and explaining
ideas clearly; and applying the mathematics we know to solve
unfamiliar problems. Participation in this variety of
mathematical activities is challenging, and for many
students, the experience will be vastly different from
experiences in more traditional mathematics course.
Goals:Our
course
is one of the General Education courses and it aims to
satisfy the following outcome objectives in the area of
Mathematics:
Students
will
demonstrate proficiency in the use of mathematics to
structure their understanding of and investigate questions
in the world around them.
Students
will
demonstrate proficiency in treating mathematical content
at an appropriate level.
Students
will
demonstrate competence in the use of numerical, graphical,
and algebraic representations.
Students
will
demonstrate the ability to interpret data, analyze
graphical information, and communicate solutions in
written and oral form.
Students
will
demonstrate proficiency in the use of mathematics to
formulate and solve problems.
Students
will
demonstrate proficiency in using technology such as
handheld calculators and computers to support their use of
mathematics.
Labs:On
Tuesdays
we will work in small groups on labs that develop the
central concepts in the course. Attendance and participation
is especially crucial on these days. You will turn in
individual write-ups of these class activities and make
presentations of your work to the other groups in the class.
It is also important to ask questions of the other groups
(who will generally work on related but slightly different
problems than your own group) when they present as you will
be responsible for all the problems on exams.
Attendance:There
may
be topics covered in class that are not in the text. You are
responsible for all material covered. I don't take
attendance, but there is a strong correlation between
attendance and final grades. Missing class more than once or
twice during the semester is likely to affect your grade,
either directly or indirectly. If you do miss class, you
should get notes and/or handouts from your classmates and/or
see me during office hours.
Homework: There are three types of homework
assignments in this class (see the homework
page for details):
Written homework will consist of a small number
of relatively comprehensive problems mostly drawn from the
Tuesday labs. The emphasis for these assignments is on
presentation and explanation.
On-line homework will consist of two
WeBWorK-based assignments each week. You are allowed six
attempts for each question and you can get partial credit
if you only get part of a problem right.These
problems will be similar to those in the book and are
graded immediately. There are over 300 problems assigned
throughout the semester worth one point each. Since this
category accounts for 250 points of your final grade,
there is significant opportunity for extra credit.
Suggested practice problems from the text are also provided
on the homework page of the class website. The
answers to most of these problems are in the text, so I
will not collect them.However, you
will see some of these problems (verbatim or with slight
variations) on tests, so completing the problems is
strongly encouraged!
The key
to success in this course is regularly working with other
students in the class, doing the homework early and asking
questions when you have them!!! We will discuss homework problems
in class, but there will often not be enough time to discuss
all of them. Please come to office hours or visit the math
tutoring lab if you have additional questions about the
homework.
Late
Policy:WebWorK assignments
will have a closing date and time and will not be accepted
late.All other work is due at the beginning of class on the announced
due date.I may accept late written
homework for reduced credit, until I have graded an
assignment or project.After I have
graded the pile, I will no longer accept late work and you
will receive a 0.I generally grade
materials within a couple days of collecting them, and
sometimes grade them the same day they are collected.Expect to lose approximately 10% for
each day an assignment is late.
Exams: We will have four in-class exams
(roughly covering Chapters 7, 8, 9 and 10), and a
comprehensive final exam. The final exam will be Monday, May
5th, from 4:15 to 6:45 pm. Make-up exams are
possible only if there is a documented
emergency.
Gateway Test: There will be a WeBWorK-based test
on basic integration techniques after we have covered
Chapter 7.You will be able to take
the test as many times as you like during the 3 week period
that it is open.A passing grade is 6
out of 7, and each problem is graded as correct or incorrect
(no partial credit).Successful
completion of the Gateway Test during the allotted time
frame is worth 2/3 of a letter grade.
Workload and Assistance:You
should expect to spend 8 to 12 hours each week
outside of class working on the course material. Some weeks
(those in which an exam is scheduled, for instance) may
require more of your time, other weeks may require less, but
on average, budget 8 to 12 hours each week. I can't stress enough that in order to be
successful in this class you should spend much of this
time working with other students in the class! Please
ask questions and seek assistance as needed. You may email me at any time, and I encourage you
to make use of my office hours and the Thursday group study
room.In addition there are two
tutoring centers (see for
hours and more information):
The math tutoring lab is
located in Ross 1250 and will open the second week of
classes. It is a great place to go if you have a quick
question or get stuck on a particular problem.No appointment is necessary.
The university tutoring
Center is located in Michener L120. It provides more
personalized one-on-one tutoring in many areas
(including Mathematics). An appointment is necessary.
Collaboration: I assume that you are here to
learn. If you talk to each other, you will learn from each
other, perhaps more than you will learn from me.I encourage you to form study groups.Try the homework yourself, and then get
together with a study group to go over questions, and to
study for tests.You will learn a
great deal from articulating your questions and explaining
material to your peers.Discussion of assigned homework is encouraged,
but you should be sure you fully understand the material
by writing your solutions on your own.Evidence
of any cheating or collaboration on work assigned to be
completed individually will result in a 0 for that work,
at minimum.
Honor Code: All members of the University of Northern Colorado
community are entrusted with the responsibility to uphold
and promote five fundamental values: Honesty, Trust,
Respect, Fairness, and Responsibility. These core elements
foster an atmosphere, inside and outside of the classroom,
which serves as a foundation and guides the UNC community's
academic, professional, and personal growth. Endorsement of
these core elements by students, faculty, staff,
administration, and trustees strengthens the integrity and
value of our academic climate. UNC's
policies and recommendations for academic misconduct will be
followed. For additional information, please see the Dean of
Student's website, Student Handbook link
Portable Electronic Devices:
Please extend courtesy to your
instructor and fellow students by turning off your portable
electronic devices, and putting them away in your bag,
during class. If you know that you may need to accept an
emergency phone call during class or if you have children in
childcare or school, please let the instructor know. If you
need to take a phone call during class, please step out of
the classroom while you complete your call.
Students with Disabilities: Students who require special
accommodations due to a disability should contact
Disabilities Support Services (351-2289) as soon as possible
to better ensure that accommodations are implemented in a
timely fashion.
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Why Is Algebra Important?
My initial reaction to the article by Mr. Cohen was that he was wrong to have written such a discouraging article to an impressionable young girl. I feel that math is important in everyday life. I do agree with Mr. Cohen in the sense that there are many aspects of Algebra that the majority of people do not use on a daily basis. I think that this fact is what leads people to the false conclusion that Algebra is useless.
To better understand our topic, let's define what we mean when we say "Algebra". Webster's dictionary defines Algebra as "a form of mathematics dealing with symbols and equations." A guest in the mathematics forum on xpmath.com states that "…the truth is that Algebra is not much more than arithmetic expanded to the point where you don't have to do trial and error to get an answer." This guest goes on to explain that "…if you view it from that perspective, and overlook the outdated nature of some problems' data, then you'll recognize that indeed math deserves a place in your career; the more competent you can become with it, the better you'll be able to competently manage you life." I wholeheartedly agree with the preceding statement. However, I'm not completely certain that math is THE MOST important subject we'll ever learn; I believe that English quite important as well.
Math describes how everything in our environment works. A working knowledge of mathematics enables us to make accurate measurements and predictions. Since Algebra uses letters to represent numbers, it forces us to leap from concrete to abstract thinking. This "new thinking" method is, I believe, the reason Algebra is so difficult for some people to learn.
It is a fact that Algebra is "essential in a huge range of occupations, including medicine, marketing, finance, economics, architecture, and computer technology. (Kollars 2008)" Even beyond it's formal mathematical applications, algebra is considered essential for developing critical thinking and problem-solving...
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Keasbey Precalculus middle school computer courses includes
- helping students their office use skills covered in their school curriculum, such as Microsoft Office (Word, Excel, PowerPoint)
- helping students in more advanced STEM (Science, Technology, Engineering, Math) coursework
- assisting m...
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Houston Algebra 2Students will also extend their knowledge of the number system to include irrational numbers, generate equivalent expressions and use formulas. Students will also start to simplify polynomials and begin studying quadratic relationships. My students will be instructed to analyze these situations verbally, numerically, graphically, and symbolically.
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Editor's Picks in Singapore Textbooks
This is a comprehensive curriculum that will give your child a solid foundation in mathematics, build up their confidence and give them a head start on their peers.
"Initially I thought of buying just the text and work books as used by the Singapore students, but the recommended workbooks in the respective Singapore Mathematics and Science grade packages are very well selected. They include solutions that are helpful for me to grade my children's work. The Mathematics teacher's Guide is colourful, but sadly the Science Teacher's Guide comes in Black & white."
This is a comprehensive curriculum that will give your child a solid foundation in mathematics, build up their confidence and give them a head start on their peers.
"Thank you so much for the very quick delivery - I wasn't expecting it for at least another week! As a mathematician and mathematics teacher who longs for the "good old days" in which pupils were given a thorough grounding in the basics underlying the subject (Algebra and Geometry), your books are a revelation! It is no small wonder that Singapore students maintain their enviable success rate in mathematics at Primary and Senior levels when your curriculum is based around such wonderful books. They are packed full of searching and thought provoking examples and investigations that do not shy away from giving pupils challenging mathematics to deal with. For this the authors are to be fully commended. It's comforting to know that some Departments of Education are willing to entertain the (remote) possibility of some partial failures in a system having high-expectations for the greater good of the discipline, its teachers and of our future mathematicians. The alternative is so often to opt for inflated grades, shallow and lack-lustre syllabi, implemented all too often solely for political favour rather than the benefit of our pupils and their development. Dr Dabbs (UK)."
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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The ACTMathematics Test is a 60-question, 60-minute test designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade
Algebra 1
Algebra 1 is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures
Algebra 2
Algebra 2 is the study of the complex number system, symbolic manipulation, and functions
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It equations
GED
The math section is 90-minute, 50-question test has two equally weighted parts, the first of which allows candidates to use calculators, while the second forbids their use. Test-takers must use the calculators issued at the testing center.
Forty of the 50 questions are multiple-choice; the other 10 use an alternate format, requiring the test-taker to record answers on either a numerical or coordinate-plane grid. Both portions of the test have questions of both types. The test booklet offers a page of common formulas as well as directions for completing the alternate-format items and using the calculator.
Geometry
The branch of mathematics that is concern with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. It also concerned with questions of shape, size, relative position of figures, and the properties of space.
To be competent with Geometry, the following topics must be understood/covered: Principles of Measurement Principles of Euclidean Geometry Cordinate and Transformational Geometry
Prealgebra
Pre-algebra is a common name for a course in middle school mathematics. In the United States, it is generally taught between the seventh and ninth grades, although it may be necessary to take this course as early as sixth grade in order to advance to Calculus by twelfth grade.
Precalculus
Precalculus bridges Algebra II and Calculus. Precalculus involves graphing with angles and geometric shapes such as circles and triangles, and finding absolute values. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations.
Probability
In math, probability is the likelihood that an event will happen. It is the ratio of the number of ways an event can occur to the number of possible outcomes.
Probability is expressed as a fraction or decimal from 0 to 1. The higher the probability of an event, the more certain we are that the event will occur.
SAT Math For grid-in questions, test-takers write the answer inside a grid on the answer sheet. Unlike multiple choice questions, there is no penalty for incorrect answers on grid-in questions because the test-taker is not limited to a few possible choices. The 20-minute section is all multiple choice, with 16 questions.
The SAT has done away with quantitative comparison questions on the math section, leaving only questions with symbolic or numerical answers.
New topics include Algebra II and scatter plots. These recent changes have resulted in a shorter, more quantitative exam requiring higher level mathematics courses relative to the previous exam
Statistics
Statistics is the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements.
In short, it is the practice or science of collecting and analyzing numerical data in large quantities.
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
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Mercer University Macon, GA (Engineering-BS)
Argosy University - Atlanta (MEd)
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About the book:
Paperback. Pub Date: 2006 Pages: 464 Publisher: John Wiley Hands-On Math Projects with Real-Life Applications. Second Edition offers an exciting collection of 60 hands-on projects to help students in grades 6 - 12 apply math concepts and skills to solving everyday. real-life problems! The book is filled with classroom-tested projects that emphasize: cooperative learning. group sharing. verbalizing concepts and ideas. efficient researching. and writing clearly in mathematics and across other subject areas. Each project achieves the goal of helping to build skills in problem solving. critical thinking. and decision making. and supports an environment in which positive group dynamics flourish.Each of the projects follows the same proven format and includes instructions for the teacher. a Student Guide . and one or more reproducible datasheets and worksheets. They all include thUsed books: 1 - 25 of 102
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hpb-round-rock via United States787981796 Publisher: Jossey-Bass, 2006 Used - Very Good, Usually ships in 1-2 business days, Very Good+ near new softcover copy with very light edgewear/rubbing, inside pages clean - no signs of wear. If any issues post-receipt, don't hesitate to contact us first- we'll quickly make it right. 98% of our media ship same or next day from Sacramento, CA.
Softcover, ISBN 0787981796 Publisher: Jossey-Bass, 2006 Used - Very Good, Usually ships in 1-2 business days, Spine uncreased; binding sound and square. Slightest of cover wear. pages clean and unmarked, including no names. Photo of the copy you are buying is included in our listing. NOT ex-library, but all proceeds benefit Lancaster PA Public Library.
Softcover, ISBN 0787981796 Publisher: Jossey-Bass, 2006 Used. This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed. Summary: "The projects in this book will enable teachers to broaden their instructional program and provide their students with activities that require the application of math skills to solve real-life problems. This book will help students to realize the relevance and scope of mathematics in their lives." -Melissa Taylor, middle school mathematics teacher, Point Pleasant Borough, New Jersey
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DALLAS, March 1 /PRNewswire/ -- Texas Instruments (TI) has released a new operating system update for its TI-84 Plus family of graphing calculators that helps educators and students make a stronger visual connection between the math in textbooks and on their handhelds.
The TI-84 Plus OS version 2.53MP with MathPrint(TM) mode enables users to input and view math symbols and formulas, including stacked fractions, in their handhelds exactly as the equations appear in textbooks.
DALLAS, July 28 /PRNewswire/ -- As the back-to-school season approaches, parents want their children to start the school year on the right foot. It's important for parents to prepare their children by offering advice and tools that will further their academic careers.
By Steele, Marcee M Introduction High school algebra and geometry teachers use graphing calculators extensively in their classes today. National and state mathematics curriculum standards recommend their use for class work, tests and assignments (Dion, Jackson, Klag, Liu, & Wright, 2001
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Basic College Mathematicsoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Basic College Mathematicsfocuses on basic number skills: operations and problem-solving with whole numbers, fractions, and decimals. Other topics include geometry, measurement, ratios, proportions, percents, and the real number system (with an introduction to algebra). The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. .
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Iselin CalculusI have taken undergraduate and graduate courses in the following discrete math topics: computer science, including data structures; linear algebra; probability theory including combinatorics; set theory and logic; number theory; calculus of finite differences; t...
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An introduction to the basic algebra normally included in a first-year high school algebra course. Includes fundamental axioms and operations applied to rational numbers, laws of integral exponents, solutions of equations, polynomials and factoring, systems of equations, graphing equations and inequalities, rational expressions, radicals, quadratic equations and applications.
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Find a Cary
...Finally, algebra 2 typically ends with complex numbers, logarithmic and exponential functions. When I teach and tutor algebra 2, I stress mathematical reasoning and multiple approaches (algebraic, geometric and numeric). For example, many students are unaware that arithmetic on complex numbers can be done on the TI83/84 calculator. Teaching them this skill gives them a way to check answers.
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Online Courses for AEA, STEP and MAT Mathematics
In addition to A level grades some universities also require students to pass Sixth Term Examination Papers, STEP or an Advanced Extension Award, AEA in Mathematics as part of their offers for Mathematics degrees. Currently (May 2014) the universities requiring STEP/AEA qualifications for their mathematics degrees are:
Online Courses
MEI provides real-time online tutorials and teaching sessions for AEA and STEP Mathematics. You can access live interactive tuition at a time and location to suit you through a platform called Blackboard Collaborate. Information is available via the STEP and AEA pages of the MEI website.
Reproduction of questions from STEP Mathematics papers in these materials is by permission of Cambridge Assessment. Other materials are used by permission of the United Kingdom Mathematics Trust.
AEA Course
Date
Topic
Session 1
Constructing a beautiful, coherent, concise argument: the proper use of notation.
Session 2
Using Series imaginatively
Session 3
Solving trig equations without getting too many or too few solutions.
Session 4
Co-ordinate Geometry: a use for GCSE Circle Theorems at last.
Session 5
Polynomials and Graphical Transformations
Session 6
Functions: how to make the simple look difficult.
Session 7
Vectors
Session 8
Differentiation Techniques
Session 9
Integration Techniques
Session 10
Unusual Questions: are they really hard?
STEP Course
Date
Topic
Session 1
Dividing by zero
Session 2
Inequalities and proof by induction
Session 3
Systematic search or proof by exhaustion
Session 4
Necessary and sufficient conditions
Session 5
Proof by contradiction and irrational numbers
Session 6
Curve sketching
Session 7
General solutions of trigonometric equations
Session 8
Differential equations
Session 9
Mechanics
Session 10
Probability
Student Comments
"The questions are refreshing and remind you that with intuition and confidence, the skills learnt at A-level are applicable to much more than repetitive exam questions. Practise of questions of this style enable a wide variety of problem solving skills to be developed and enjoyed."
"I really enjoyed the lessons and felt challenged all the time. I always felt I had achieved something every lesson, and it made me more confident in taking both STEP and AEA."
Register with the FMSP
Schools and Colleges can submit an online request to register with the Further Mathematics Support Programme. It is free to do so and there are many benefits.
FMSP Regions
To find out about the FMSP in your area please select a region from the map below:
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This is the free version of "Function Plotter". Completely free and without advertisements.This app, is able to draw multiple function graphs, calculate function values and value tables. It's also possible to integrate functions numerically.The following mathematical functions are available:polynomials, rational functions, trigonometric functions, inverse trigonometric functions, hyperbolic functions, natural logarithm, exponential function and all the possible combinations of
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20Math In Our World, Media Update
Math in Our World
Student Solutions Manual to accompany Math in Our World
MathZone Access Card for Math in Our World
ConnectPlus by ALEKS Access Card 52 Weeks for Math in Our World
Customer Reviews
very goodMarch 16, 2011 by Karen
This is a worth getting textbook. It is very simple and easy to understand. I was interested in the contents, and was not disappointed. The author offers many useful examples to illustrate every concept. I bought this textbook for a course and it arrived in a good condition and the price is reasonable. Thank you.
Summary
The author team of Dave Sobecki, Angela Matthews, and Allan Bluman have worked together to create the second edition of Mathematics in Our World, an engaging text catered to the needs of today's liberal arts mathematics students. This revision focuses strict attention to a clear and friendly writing style, integration of numerous relevant real-world examples and applications, and implementation of the step-by-step approach used for years in Bluman's Elementary Statistics: A Step by Step Approach. The result is an exceptionally engaging text that is able to both effectively and creatively convey the basic concepts fundamental to a liberal arts math curriculum for even the most hesitant student.
Table of Contents
Problem Solving
The Nature of Mathematical Reasoning
Estimation and Interpreting Graphs
Problem Solving
Chapter 1 Review
Sets
The Nature of Sets
Subsets and Set Operations
Venn Diagrams
Using Sets to Solve Problems
Infinite Sets
Chapter 2 Review
Logic
Statements and Quantifiers
Truth Tables
Types of Statements
Logical Arguments
Euler Circles
Chapter 3 Review
Numeration Systems
Early and Modern Numeration Systems
Tools and Algorithms in Arithmetic
Base Number Systems
Operations in Base Number Systems
Chapter 4 Review
The Real Number System
The Natural Numbers
The Integers
The Rational Numbers
The Irrational Numbers
The Real Numbers
Exponents and Scientific Notation
Arithmetic and Geometric Sequences
Chapter 5 Review
Topics in Algebra
The Fundamentals of Algebra
Solving Linear Equations
Applications of Linear Equations
Ratio, Proportion, and Variation
Solving Linear Inequalities
Solving Quadratic Equations
Chapter 6 Review
Additional Topics in Algebra
The Rectangular Coordinate System and Linear Equations in Two Variables
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This excellent site, from LessonCorner, helps educators create customized math worksheets for students of all levels. Creating worksheets is free, and visitors can also name them what they wish and print them to...
Created by Lang Moore and David Smith of the Connected Curriculum Project, this module continues the study of polynomial approximations to functions, concentrating on the region of convergence. This is one within a...
This site from Northern Illinois University provides online notes for students using the Abstract Algebra textbook (which is also available online). The materials cover the topics of integers, functions, groups,...
This is the third topic in the series of lessons on math provided by DeafTEC. Gary Blatto-Vallee, a math and science instructor at the National Technical Institute for the Deaf, guides viewers through a variety of...
This algebra lesson helps students explore polynomials by solving puzzles. The activity explains the relationship between expanding and factoring polynomials, as well as factoring trinomials, and multiplying monomials...
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Description
PP Maths is an application which allow students and parents to see the test marks, announcement, topper's list. Students can download notes (solutions) using this app. NOTE: This app is made for Prof. Prasanna Pandit and has been developed by Knowledge PortalThis application allows to download Papers Collection of 10th and 12th standard (S.S.C. and H.S.C.).
Simply Gujarat Secondary and Higher Secondary Board provides Previous year Paper Sets. The main intention behind creating this app is you can easily and quickly download any year of examination papers10th Science Animated explains concepts of GSEB 10th Science by means of animation and speech. Watching animations and hearing sound are far better than reading textbooks for quick learning. Content of the app is planned as per syllabus of GSEB 10th Science chapter Four. Part two of the app includes following points.
Are you study in 12th standard then start learning with this application. In the quiz there are multiple questions related to 12th science student who are preparing for GSEB board exam. Compete with your friends and see who has better knowledge about Physics After completing test you get score and also display no of right and wrong answer. * Features: • Attractive User Interface • Rich set of questions chapter wise • Each category contains 15 questions which will be generated randomly. • After completing test score will be display. • Random questions each time you play the quiz"17 2.Application's of Gauss's Law 3.Illustration-20 4.Electric Field Due to a Uniformly Charged Infinite Plane Sheet or Sheet of Charge 5.Illustration-21 6.Electric Field Due to a Uniformly Charged Thin Spherical Shell 7.Electric Field Intensity Due to Uniformly Charged Sphere3 2.Coulomb's Law in Vector From 3.Forces Between more than two Charges : The Superposition Principle 4.Illustration-5 5.Illustration-6 6.Electric Field
Are you study in standard 12th? Then start learning with this application. In the quiz there are multiple questions related to 12 th science student who are preparing for GSEB board exam. Compete with your friends and see who has better knowledge about Chemistry
* Features: • Attractive User Interface • Rich set of questions for various categories. • Each category contains questions which will be generated randomly. • Categories are display chapter wise. • After completing test score will be display. • Random questions each time you play the quiz"
Features - Based on Gujarat Board Course - Question are in Gujarati Medium - Each Chapter Contains 100+ Question - With Animations & Sounds to Make PractAbout Us Sarvayogam School begins with blessings of Param Poojaya Shree Yogeshwarji and Param Poojya Maa Sarvasawari Sarvayogam school started the journey to discover the talents of Students in the year of 2002. Sarvayogam School is recognised by the Government of Gujarat (GSEB). Sarvayogam School is co-educational English medium school , run by Maneklal Patel Charitable Trust. Vision Our vision is to train young ones under full protected place which allows them the freedom to transform themselves to their full glory. At Sarvayogam children are treated with utmost care and responsibility with value based education. Mission Learned experienced qualified and kind hearted teachers who motivate students to reflect to respond and to be creative. They make the students more responsible and increase their level of confidence . Pays equal and close attention to all students. Make the teaching work interesting not boarding to achieve goals. Pioneering foundational work done at pre-primary levels also. Teaching & Learning All the basic concepts are taught through multi modal instruction. Such as worksheets, class activities, projects , games , so that the concepts are embedded in the child's mind before we expand the concepts to the next level. Our students are prepared for the academic challenges that await them with our expert teachers. Our teachers strongly believes in the right blend of tradition and modernity. We have developed our own books , based on actual syllabus. Management Managing Trustee Mr. Siddharth Patel A Post Graduate in Accountancy and MBA in Human Resource Management. Academic achievements Year 2013- 2014 S.S.C. Result 100 % Out of 61 students 24 students scored above 90% percentile rank Social Work Sarvayogam School students have cancelled their picnic and distributed full kit of two months grocery to sixty diamond workers families at Bapunagar. Every year at the end of Academic year students collect their used books and notebooks and from that collected amount :
Donate : Soap and body lotion to Observation house and Blind association Two tricycles given to physical handicapped association.
10th Science Animated explains concepts of GSEB 10th Science
Content of the app is planned as per syllabus of GSEB 10th Science chapter one. Part two of the app includes following points.
Bakibol Carbon Nanotube Properties of Nanotube Glimpses of the Benefits of Nano Technology to Mankind Importance of Nano Technology
Animated biology explains concepts of biology by means of animation and speech. Watching animations and hearing sound are far better than reading textbooks for quick learning . We made learning of biology easy via applications like this. There are many other apps on store with "Sparrow education" name, and few more will be uploaded soon. This apps are very useful for students of 12th science (HSC) in Gujarati medium. You can use this app on your smartphone or tablets.
Content of the app is planned as per syllabus of GSEB 12th standard biology chapter one. Part three of the app includes following points.
---> Vayurandhra open close process ---> Transpiration ---> Transport of water in plant ---> How do plants absorb water
The Examiner is an MCQ based software which has been designed and tailored specially for the students to have smooth functioning of Examination Practice. We believe that, The Examiner will work as the most smartest software to practice MCQs. It enables concept clarity, rational thinking ability and analytical skills of the students. Moreover, it lets students embrace themselves. Features: • No internet connection required. • Supported with innumerable Question Bank • Customized tests to suit school curriculum. • Blue print, to set chapter wise importance. • Practice questions in accordance to Chapter, Topic or Level. • Exam / Practice Mode. • Practice of wrong attempted questions in earlier exams. • Get review of each question along with detailed solutions. • Summary, detailed and analytic reports. The Examiner : Available in Android and Desktop Version for GSEB – Class 09 to 12 (Eng/Guj Medium) || CBSE– Class 06 to Class 10 || JEE Subject Offered : Physics, Chemistry, Biology, Maths, Science, Social science, English, Gujarati
Bored of reading textbooks for hours and hours? Want to make your studying more interactive and interesting? Want a simple, fun, portable method of study? Then look no further than the Biology Quiz app.This app has a database of questions related to 11 th science student which can be used for practicing exams like GSEB Board,medical entrance etc. This app cover all syllabus of 12 science biology Define by GSEB.At the end of each completed unit, the user is given their score and the option of either keep playing or quit the game. The answers are also available at a time when user plays quiz.
With a variety of events revolving around a common theme, SPACE is an attempt to bring the best out of students.The festival kicked off in the year 1981, and its never looked back since then. The student council is largely responsible for making the festival bigger and more successful than the previous year's.
SPACE has always been the home for various competitions. Be it singing or dancing, street play or street dance, rink football or guitar-showoffs, the stage has always seen talented performers battle it out for the prizes and of course, for appreciation from the ever enthusiastic crowd. Over the years, the festival has gained such a reputation that students from other colleges actively look forward to participating in the competitions every year.
During the course of the day, along with these competitions, there are also a lot of fun-events going around in the college. Quizzes, treasure hunts, karaoke, wall painting and more, ensure that anyone who walks in has his or her share of fun before going out.As the day passes on, the evenings call for the special events which are often the main highlights of SPACE. We have professional artists, rock bands, DJs performing on these evenings to ensure that the everyday ends with a bang!
Apart from this, SPACE also gives a fantastic opportunity to the in-house students to try their hand at organizing events and managing people. An opportunity which our students always make the best of. Each year, we see students improvise their creative skills to come up with something sensational.
Besides, there is also an increased response in the number of students who are willing to be a part of the organizing team every year. That just goes on to show how dedicated our students are for the cultural fest, which lasts for three days but leaves a lasting impact on the students' minds for a long time.
Aksh Tutorials and pvt tuition is the only tutorials which care and take the students
Aksh has produced many doctors, engineers, pharmacist, teachers, scientists etc.
Aksh Tutorials and pvt tuition is the only tutorials which care and take the students Aksh has produced many doctors, engineers, pharmacist, teachers, scientists etc.
Dr. Panjabi's Biology Tutorials is an application which allows a student and parent to see the test marks, announcement, topper's list. Students can download notes (solutions) using this app. NOTE: This app is made for Dr. Vishal Panjabi and has been developed by Knowledge Portal.
At Ravi Avinash Tutorials we aspire to give our students the best education. We provide a study centric and focused environment for the student to concentrate and clear his concepts. This study pattern not only enables a student to clear the examinations but also lays the foundation for all career paths, such as engineering, medicine, research etc…
Ravi Avinash Tutorials offers a wide mix of various courses which include 11th Standard, 12th Standard, NEET and Test Series. With an online test series, electronic arithmetic systems, CCTVs, seminars before and after course, 35-40 students in a batch and thrice a week lectures, Ravi Avinash Tutorials provides the right environment and learning experience to nurture a prosperous career and future of your child.
We also believe in knowing our students and their parents well. In order to achieve this we have a dedicated back office team whose sole responsibility is to update you regularly on the progress of your child.
ACE chemistry private tuitions is a professionally managed private tuition, headed by Mr. Santosh Yadav, the founder and heart of the class. The coaching epicenter is based in Mulund. ACE chemistry private tuitions focuse on H.S.C & CET coaching in Subject of Chemistry. Detailed notes as well as its rigorously unique test series has enabled it to be the only, one of the most fastest growing chemistry private tuitions in its league to train students and produce 'ACERS' in Chemistry . A high degree of standardization of the course delivery and teaching methodology ensures that the student experience remains the same throughout entire span of learning.
ACE CHEMISTRY 2.0 is an application which allows a student and parent to see the test marks, announcement, topper's list. Students can download notes (solutions) using this app. NOTE: This app is made for Prof. Santosh Yadav and has been developed by Knowledge Portal.
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Introduction to Differential Geometry - Volume two
Pros:clear, gradual introduction of the important notions, lots of pictures.
Cons:none
A Comprehensive Introduction to Differential Geometry" is a 5 volume book on Differential Geometry published for the first time in the seventies. In this review I intend to give a description of the second volume alone; the other volumes either have been already reviewed or they will follow shortly.
If you didn't already read my review about the first volume I suggest you do ( like any other book these volumes are related. Still I will try to give an independent opinion on this second volume and to make reference to the first one as little as possible.
Roughly speaking, the first volume described the manifolds and their differential properties (vectors, tensors and a little bit of calculus on these manifolds). This second volume is more geometric than the first one. First you learn about curves and surfaces in 2 and 3 dimensions in Euclidean space; then, same thing is presented in the light of manifolds. This leads to the notion of curvature, an essential one in Differential Geometry. The rest of the book is dedicated to it (properties, identities, special cases, etc.). As usual I will give a brief description of each one of the chapters.
Chapter one - Curves in the Plane and in Space: This chapter is concerned with curves in an Euclidean space (R^2 or R^3). You will have a chance to remember the things you already knew from Calculus and to learn new stuff; everything is presented with an eye on the curvature and torsion notions. Again I was surprised by the clarity of the text and by the abundance of pictures. There is an average of two pictures on every page! And that's a very good thing when you learn geometry.
Chapter two - What they knew about Surfaces before Gauss: This is the shortest chapter of the book (I guess they didn't know too much before Gauss; by the way there is an interesting story about Gauss at the end of the review). It contains two theorems Euler's and Meusnier's with proofs, pictures and explanations.
Chapter three - The curvature of Surfaces in Space: This chapter goes deep in the theory of surfaces. The Gauss map is introduced and it leads smoothly to the notion of Gaussian curvature (this is the one that gives us that the plane has a zero curvature and the sphere has a positive curvature equal to 1/r^2 where r is it's radius). The fundamental forms are presented with the use of Weingarten map. Also you will have a chance to calculate the geodesics of some of the most known surfaces: plane, sphere, cylinder etc.
Chapter four - The curvature of the higher dimensional manifolds: This chapter has a very interesting and unique structure. It starts with a lecture given by Riemann on October 10, 1854 at Gottingen University. It was one of the most important events in Differential Geometry. At first it looks impossible to follow, but in the next section the author explains every little notion of that lecture and show how Riemann's ideas inspired manifolds and the tensors that is named after him (Riemann's curvature tensor).
Chapter five - The absolute differential calculus: All the calculus we've done so far was, in a way or another local. the defined derivatives usually depended on tangent vectors. In this chapter the covariant (or absolute) derivatives are defined and used to obtain Ricci's identities, the torsion tensor and Bianchi identities.
Chapter six - The dell operator: This section presents some of the most important connections (derivatives) on manifolds, Koszul and Levi-Civita. The notion of parallel translation (or transport) and how to explain the torsion and the curvature tensors in terms of it is also in this chapter.
Chapter seven - The moving frame: The structural equations for the Euclidean space introduce the ones for Riemannian manifolds (Cartan's). These are also given in some adapted frames as well as in polar coordinates. The chapter has also some short presentations on some subjects of interest: Manifolds of Constant Curvature, Conformally equivalent manifolds, Normal Coordinates.
Chapter eight - Connections in principal bundles: An important derivative is presented in this chapter namely the Lie derivative. It is introduced by means of the principal bundles. Covariant differential, curvature form, structural equations and the torsion and curvature tensor are also presented from this point of view.
Conclusions: This second volume goes deep in the differential properties of the manifolds. The most important things to learn from it are the curvature tensor and the connections on manifolds. Again I was amazed by the clarity of writing and by the numerous examples and pictures. There are no exercises in this volume.
Short story about Gauss 1777-1855: Some mathematicians thing Gauss was the greatest mathematician ever. Some think he was a fraud. But at least everybody accepts the fact that he was the most well know mathematician in his life time. A lot of young mathematicians wrote to him saying that they thought they discovered some new things and would like Gauss to take a look at them. Gauss would read the manuscript and reply either that it's useless or that he also looked at these kind of problems and found such and such. Some say that he was just stealing the poor guys work; some other say that he was just brilliant and knew a lot. Some of the things attributed to him are: the theory of curves, the fundamental theorem of Algebra, curved geometry. But, as the X files always say, The truth is out there.
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This is a textbook for upper-level economics students who need to study mathematics. The authors present the concepts by applying them closely to the economics students will need to study. Diagrams and a range of exercises reinforce what students have learned in each chapter
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This is a Power Point presentation with audio which I have designed for my Pre-Calculus Algebra students to help them better...
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This is a Power Point presentation with audio which I have designed for my Pre-Calculus Algebra students to help them better grasp the terminology and concepts of parabolas. In this presentation, students can regulate the flow of information as they wish. I would like to thank Nancy Doolittle for her technological assistance with this Point presentation on Parabolas with audio to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Power Point presentation on Parabolas with audio
Select this link to open drop down to add material Power Point presentation on Parabolas with audio Needle Estimate of Pi (Mathematics) to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Buffon's Needle Estimate of Pi (Mathematics)
Select this link to open drop down to add material Buffon's Needle Course on Complex Numbers to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Dave's Short Course on Complex Numbers
Select this link to open drop down to add material Dave's Short Course on Complex Numbers to your Bookmark Collection or Course ePortfolio
The aim of these investigations is not to provide drill (although links to other resources on the web that do have been...
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The aim of these investigations is not to provide drill (although links to other resources on the web that do have been included in places), but to encourage students to think about why things happen the way they do in calculus. Such an understanding can be greatly useful both when rote memorization fails and when studying a new concept. Indeed, many concepts from the single variable calculus studied in APSC 171 form the foundations of later courses. The investigations have been designed to be quick and self-contained and should take at most ten or fifteen minutes each to completeQ's (applets for calculus) to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material MathQ's (applets for calculus)
Select this link to open drop down to add material MathQ's (applets for calculus System of Equations with Application to Matrix Inversion to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Solving System of Equations with Application to Matrix Inversion
Select this link to open drop down to add material Solving System of Equations with Application to Matrix Inversion to your Bookmark Collection or Course ePortfolio
Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra,...
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Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra, Trigonometry, PreCalculus, Calculus or Statistics and enter a problem. The computer solves the problem and shows the steps for the solution. It also has a worksheet generatorway to your Bookmark Collection or Course ePortfolio
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math...
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice (Math Portion) to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Khan Academy (Math Portion)
Select this link to open drop down to add material Khan Academy (Math Portion Trigonometry Wikibook to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Trigonometry Wikibook
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Purplemath contains lessons, links, and homework tips, all designed to help the high school or college algebra student find...
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'In writing Elementary Algebra, John Redden had simple but important aims:Lay a solid foundation in mathematics through...
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'In writing Elementary Algebra, John Redden had simple but important aims:Lay a solid foundation in mathematics through algebra, the basis of all mathematical modeling used in a variety of disciplinesGuide students from the basics to more advanced techniques in mathematics PEDAGOGICAL FEATURES:REAL WORLD APPLICATIONS:With diverse exercise sets, students have the opportunity to solve plenty of practice problems. Elementary Algebra has applications incorporated into each and every exercise set. John makes use of the classic "translating English sentences into mathematical statements" subsections in chapter 1 and as the text introduces new key terms.VIDEO EXAMPLES AND ACTIVITIES:Embedded video examples are present, while the importance of practice with pencil and paper is still stressed. This text respects the traditional approaches to algebra instruction while enhancing it with today's technology.OPEN AND MODULAR FORMAT:While algebra is one of the most diversely applied subjects, students find it to be a difficult hurdle in their education. With this in mind, John Redden wrote Elementary Algebra in a format that allows instructors to modify it and leverage their individual expertise and maximize student experience and success.MORE VALUE AT AN AFFORDABLE PRICE:Using the online text in conjunction with a printed version of the text could promote greater understanding (at a lower cost than most algebra texts
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The study of mathematics forms the basis of logical thought and problem solving. In an increasingly technological world, the knowledge of how mathematics is applied to present day problems is as important as the skill to apply these mathematics. Math courses are intended to show the student the variety and depth of the topics where mathematics has made a significant impact in our present day world and to give them an appreciation for the power of mathematics as a problem-solving tool. The following core values are fundamental to all math courses:
Appreciating the usefulness of mathematics in understanding the real world.
Recognizing the application of mathematics to other fields of study.
The Math Department's Curriculum includes: Algebra I, Algebra II and Honors Algebra II, Geometry and Honors Geometry, Pre-Calculus and Honors Pre-Calculus, Calculus and AP Calculus, Statistics and Honors Statistics, and Discrete Mathematics. This curriculum provides all cadets with a solid mathematics foundation to pursue their college degree of choice whether it be the math intense programs found at our nation's service academies which several of our graduates attend or the diverse offerings found throughout the prestigious colleges in Virginia that are well attended by our graduates.
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Appcast for GSP5
version history with a sparkle via iusethis.comen-us0 Geometer's Sketchpad® is the world's leading software for teaching mathematics. Sketchpad® gives students at all levels—from third grade through college—a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. Make math more meaningful and memorable using Sketchpad.
Elementary students can manipulate dynamic models of fractions, number lines, and geometric patterns. Middle school students can build their readiness for algebra by exploring ratio and proportion, rate of change, and functional relationships through numeric, tabular, and graphical representations. And high school students can use Sketchpad to construct and transform geometric shapes and functions—from linear to trigonometric—promoting deep understanding.1geometry maths drawingSharewareGSP5 5.0.4
Version: 5.0.4No changes specified]]>62396Fri, 03 May 2013 14:30:25 -0000not specified
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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Linear algebraHave you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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More About
This Textbook
Overview
The p-adic numbers and more generally local fields have become increasingly important in a wide range of mathematical disciplines. They are now seen as essential tools in many areas, including number theory, algebraic geometry, group representation theory, the modern theory of automorphic forms, and algebraic topology. A number of texts have recently become available which provide good general introductions to p-adic numbers and p-adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf by providing a collection of intermediate level articles on various applications of p-adic techniques throughout mathematics. The chapters will be especially useful for graduate students beginning research in these areas, and the contributors have been encouraged to write at a level suitable for this purpose.
Editorial Reviews
Booknews
A collection of ten intermediate articles for graduate students of mathematics just beginning their own research. Surveys the application of p-acidic numbers and analysis in such fields as number theory, algebraic geometry and topology, group representation, and automorphic forms
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These activities use the Function Analyzer tool to reveal the connection between symbolic and graphic representations in equation solving. The document includes a series of exercises for single equati... More: lessons, discussions, ratings, reviews,...
Explore how the parameters in a quadratic equation in vertex form affect the graph of the equation. Dynamically change the parameters and immediately see how the graph changes. Try to change the par... More: lessons, discussions, ratings, reviews,...
An applet essentially mimicking a graphing calculator, this is used in a number of activities from the same author. Graph functions, experiment with parameters, distinguish between functions by graphi... More: lessons, discussions, ratings, reviews,...
This applet, created with Java Sketchpad, allows the exploration of a parabola in standard form, where the coefficients a, b, and c are restricted to multiples of 1/2. A sister sketch allows unrestri... More: lessons, discussions, ratings, reviews,...
Solving sine equations. This shows a sine curve that can be manipulated and a horizontal red bar that moves up and down. Students are given equations to solve, like sin x = -.5. They graph sin x and t... More: lessons, discussions, ratings, reviews,...
The "Scrambler" is an amusement park ride with a central rotating hub with three central arms, with spokes at the end of each arm that rotate in a different direction. This applet, approved by the El... More: lessons, discussions, ratings, reviews,...
Use this savings calculator to see how a consistent approach to investing can make your money grow. Whether saving for a house, a car, or other special purchase, the savings calculator will help you d... More: lessons, discussions, ratings, reviews,...
This is a full lesson that gives students experience with exponential functions in an application format. There is a movie, an applet for gathering information, and a graphing applet. There is a les... More: lessons, discussions, ratings, reviews,...
The applet below is a simulation of the law of radioactive decay. The red circles of this simulation symbolize 1000 atomic nuclei of a radioactive substance whose half-life period T1/2 amounts to 20 s... More: lessons, discussions, ratings, reviews,...
The "Exponential Decay" Java applet was used on the discussion board with an online Algebra II course. Students were asked to use the applet, and then go to the discussion board and discuss the questi... More: lessons, discussions, ratings, reviews,...
The user will create their own set of data and then see how changes can occur in the mean, median, and mode and the shape of the histogram when changes are made in the data set in this activity.
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This document contains objectives, guidelines for lectures, and materials needed to instruct advanced high school mathematics students in the basic structure of fractals, the algorithms involved in creating fractal pictures, fractal dimension, and leading them in a research project where they will investigate the basic properties and algorithms involved with fractals.
Fractals are a "hot" topic recently. Throughout this seminar I was given the opportunity to examine how fractals and chaos are present all around us in nature. Some of the mathematics that I teach on a daily basis goes back as far as 300 B.C. with Euclid and his work with geometry. My students are always asking why are we learning a certain mathematical lesson or when will we ever use this again. They feel as though the mathematics they are learning is from the past and they are just going through the motions of solving a problem. It will be beneficial for me to share with my class a new and more recent mathematical topic.
This unit of study on fractals will be incorporated into my 10th grade Gifted (Center of Advanced Studies – CAS) Algebra 2 class. The purpose of this unit is to introduce students to the topic of fractals. In teaching a gifted class, it is expected that I add enrichment into the existing curriculum. It is my job to introduce students to topics other than ones that are present in their textbook. I should be able to expose them to mathematical topics that are present in the real-world so they can see the relevance in them. Hopefully my students will enjoy doing the mathematics necessary to develop a fractal as well as seeing that fractals are beautiful geometric shapes.
From Order to Chaos and Back Again Adam P. Deutsch Taylor Allderdice High School
Chaos is one of the most important scientific/mathematical discoveries in recent years and is truly changing the way experts think in such diverse areas as physics, business and economics, biology, sociology, meteorology and many others. And it is an exciting new branch of mathematics. The results are surprising and relevant and ultimately beautiful. And one of the best things about chaos theory, at least from the perspective of a high-school mathematics teacher is that the mathematics which lies at the foundation of chaos theory is very basic. Ultimately, it is arithmetic. Some algebraic notation makes it easier to work with and represent, but at the most basic level, it's all about arithmetic.
The purpose of the unit described herein is to provide students with the opportunity to explore the foundations of the mathematics of chaos. This unit will introduce students to the mathematical process that was first discovered to lead to chaos – iteration. And from there, they will explore the underpinnings of this new branch of science.
Fractals and Chaos in the English Classroom J. Gary Dropcho Carrick High School
An English teacher taking a seminar on fractals and chaos seems random, but a closer look reveals an intersection of patterns between science and literature. Studying the science of chaos and its recursive figures of self-similarity is an interesting way into some of the literature read, discussed and written about in an accelerated twelfth grade English class.
Making the Connection with the Sierpinski Triangle Jane H. Fraser Pittsburgh Classical Academy
Fractals are geometric shapes that are self-similar at different scales. The Sierpinski Triangle is one of the most well-known and versatile of all fractal figures. The possibilities for rich mathematical explorations and connections are numerous. The middle school Connected Math Program, currently taught in Pittsburgh Public Schools, is devoted to developing student knowledge and an understanding of mathematics that is rich in connections.
I have designed a unit that explores many of the intricacies of the Sierpinski Triangle while allowing students to revisit and discover numerous math concepts, such as measurement, fractions, and area. This unit is particularly suited for the seventh grade curriculum, with its emphasis on similarity and scale factor.
This curriculum unit is quite unique in the fact that it explores four content areas mathematics, science, technology and art. These wonderful blends of subjects make the activities exciting. I have taken the Gestalt learning theory; best teaching practices and related to the reason my student's development. I wonder why anyone has not noticed a fractal. Would it be because it is not in their life space? I will discuss this in detail. The whole concept of fractals and chaos are very new. This very new subject has all of the content areas I have included in it. You will find that most early childhood classrooms will be able to use this unit. I have taken some specific strategies to bring about an understanding of the recursive patterns of a fractal. I have also included an activity to understand chaos. This is through a kindergartener's eyes. I have included family involvement and an interesting field trip. I do believe that the intermediate elementary classes as well can use it. Take your time and discover as my students will do and you will find it to be fascinating.
Fractals, Chaos and Brain Functioning Eric Laurenson Peabody High School
My first introduction to fractals, unbeknownst to me, involved my early fascination with drawing leafless trees. As a child, I would incessantly draw the intricate, repetitive, but not identical patterning of a tree's trunk, boughs and branches. I recognized the necessity of making the branches curve, split and shrink in scale in a controlled but not entirely predictable fashion. In effect, this was an introduction to fractals with a sense of chaos. Fractals demonstrate a repetitive scaling that makes them identical on all scales, whereas chaos introduces a seemingly random aspect to the patterning. It wasn't until I took this class on fractals and chaos that I realized how pervasive fractal patterns are in nature, that I was seeking those patterns at an early age and that in the midst of that attraction to pattern was an innate sense that chaos provides a divergence from that pattern.
This unit is intended to introduce the pervasive concepts of fractals and chaos to high school physics students. The unit will provide the mathematical and conceptual ideas for a teacher to be able to present the unit. The level of the unit can be tailored to suit any level of physics class from general to A.P. The unit is meant to be included as a part of the modern physics curriculum but also can be included to supplement the mathematical concepts of a high school physics course. The information on brain functioning is meant to add relevancy to the topic. Brain functioning is meant to stimulate interest in the challenging concepts of chaos and fractals. Although this unit is intended for high school physics it is my hope that teachers in other areas who wish to explore brain functioning, chaos or fractals may find this unit engaging. This could potentially include Biology teachers who are introducing the issue of brain function. I can also imagine this unit being used for the mathematical content on fractals and chaos. The unit could also be utilized by any teacher who wants to introduce the concept of chaos and finds the connection to brain functioning engaging.
Chaos theory (Mathematical) is enrichment to teaching Ecology and General Science. The collaboration (science and mathematics) will show students the integral relationship between the two disciplines. The primary example, in ecology, is to use population studies to explain the use of Chaos theory. This unit maybe used separately or part of the study of population growth in the past or future. This unit will help students understand old explanations of population. Also, the unit will help students use logistic equations to analyze population growth. Furthermore, it will give students a way to use computer analysis of old or new data to show how Chaos theory can be applied.
Fractals and Chaos an Introductory Unit Joseph McGuire Oliver High School
The following unit is intended for Biology students in grades 9 through 12. The unit deals with the subject of fractals and chaos. The unit covers mainly fractals that are found within nature. Students are required to construct fractals. Students are also required to identify fractals that can be found within the environment. Students will also get a brief history of the contributors that led to the study of fractality and chaotic systems. Students are required to use math within the unit that satisfies the district's math standards as well as address math anchors required by the various disciplines. Students will be required to write on the subjects covered as well as do research that deals with the subject matter. Pattern recognition and creativity will be explored within this unit. Upon completion of the unit students will have a working vocabulary that reflects the subjects of chaos and fractals.
This unit on Fractals will be used within a Geometry unit, to expand and enhance the concepts that are learned in Basic Geometry. Fractals are the study of the roughness of the world, its transformations and dynamical changes. Fractal Geometry studies the geometry in nature and the changes that take place all around us.
So what is a fractal? What does one look like? Who first coined the term? How can elementary students be taught to understand their significance?
Through interactive, engaging, and sequential activities on fractals, the student will develop a basic understanding of how fractals explain mathematical connections to nature. For some students, the knowledge will plant a seed for future investigations.
This unit is meant to be supplemented into a high school chemistry course in order to introduce chaos and fractals to students and show its relevance to real life. The unit may be helpful for students in grades 10 – 12 in a regular education or inclusion chemistry classroom. The chaos theory can be related to entropy in chemistry and everyday life. This unit can also be tied into the exchange of energy in a chemical reaction, and may help further define the properties associated with both endothermic and exothermic reactions. Mathematics and science both are more meaningful when they are rooted in real-life contexts. This unit will allow students the opportunity to become actively involved in learning, they will be given the chance to both visualize the motion of particles in chemical reactions and also see the how fractals form in a single replacement reaction. This will allow them to visualize how the particles rearrange themselves in a seemingly chaotic way, and make connections both to the chemistry and the math behind the reaction they will be seeing.
This unit on Fractals was written for a Middle School Saturday Program but can be used in addition to any regular curriculum. It starts with the basics of what a fractal is and lets students explore different fractal patterns. As students are introduced to different simple fractals they begin to recognize the pattern and try to continue to expand it. They will explore similarity of the changing shape and perimeter in some cases. They will try to appreciate both the simplicity and complexity of the pattern leading them towards creating tables and equations represented by the fractals.
As a teacher I hear complaints and groans when it is time for Math. I feel that many students dislike Math because they do not understand it. I chose to create a unit about fractals that is brought down to the fourth grade level. My main priority for this unit is to spark an interest in Math in students by integrating the teaching of fractals into other subjects. I also want students to get enthusiastic about learning about Math so that they are willing to learn more.
This unit includes an introduction about fractals. The following lessons integrate the teaching of fractals into Math, Science, Writing, Computers, and Art. This unit takes a "hands-on" approach to teaching about fractals.
My theory is that when students are able to see and touch objects related to what they are learning they are better able to grasp the concept. By getting students involved in the process of learning I am hoping they will be encouraged to want to learn more about the mathematical concepts of fractals. Learning the basics about fractals will lay the groundwork for other math ideas.
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Home >
Mathematics >
Which OCCC general education math class is best for you?
Which OCCC general education math class is best for you?
The OCCC math department currently offers four classes that satisfy the college's general education requirement: College Algebra, Precalculus, Contemporary Math, and Introduction to Statistics. Each of these courses was developed to satisfy particular needs. To decide which one is best for you, compare each class's design to the needs of your degree program.
Important: Whichever course you choose, check that it will transfer to the four-year school of your choice. For the Oklahoma Regents Transfer Grid, go to:
Math 1503 - Contemporary Mathematics
Prerequisite: (R) (W), MATH 0403 or adequate Math Placement Test Score, either within the last year.
3 CREDITS A study of the mathematics needed for critical evaluation of quantitative information and arguments (including logic, critical appraisal of graphs and tables); use of simple mathematical models, and an introduction to elementary statistics.
This course is meant for students who plan to enter degree fields that will require little (if any) formal mathematics. It is a survey of the modern use of mathematics. It is often taught through hands-on projects.
Example degrees: English Performing and Visual Arts History
Math 2013 - Introduction to Statistics
Prerequisite: (R), MATH 0403 or equivalent or adequate Math Placement Test Score, either within the last year.
In this course, you will .learn how to summarize and analyze data collected from surveys and experiments. You will also learn to make and effectively comm communicate conclusions based on data. This information is helpful in analyzing information you receive through newspapers, magazines, TV, radio, and journals.
Example degrees: Psychology Journalism Political Science
Math 1513 - College Algebra
Prerequisite: (R), MATH 0403 or adequate Math Placement Test Score, either within the last year.
3 CREDITS The student will demonstrate an understanding of the general concepts of relation and function and specifically of polynomial, exponential, and logarithmic functions; the ability to solve systems of equations by utilizing matrices and determinants; and the ability to solve practical problems using algebra.
This course was designed to prepare students for a degree in fields that require some mathematical knowledge beyond that usually taught in the developmental math sequence, but does not require any of the engineering calculus sequence (Math 2014, Math 2214, Math 2314). It is a preparatory class for Calculus for Business, Life Sciences, and Social Sciences (Math 1743), as well as many science courses.
Example degrees: Business Biology Chemistry
Math 1533- Precalculus and Analytic Geometry
Prerequisite: (R) (W), MATH 0403, or adequate Math Placement Test Score, either within the last year.
3 CREDITS This course is intended to serve students for whom Calculus and Analytic Geometry I is a requirement. Topics will include conic sections, systems of equations (both linear and nonlinear), and a general discussion of functions with emphasis on polynomial, rational, exponential, and logarithmic functions.
This course was designed to prepare students for success in the engineering calculus sequence (Math 2014, Math 2214, Math 2314).
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"the study of linear algebra, the theory and practice of analyzing linear relations and their behavior under linear transformations. Practically every modern technology relies on linear algebra: simplifying the computations required for internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between. Five major topics are addressed: linear systems of equations, vector spaces, matrices and linear transformations, determinants, similarity, and eigenvalues. This free course may be completed online at any time."
"One of the biggest challenges in teaching science, technology, engineering, and math is capturing the students' imaginations long enough for them to see all of the possibilities that lie ahead," the company wrote on the Learn with Portals site. "Using interactive tools like the Portal series to draw them in makes physics, math, logic, spatial reasoning, probability, and problem-solving interesting, cool, and fun, which gets us one step closer to our goal-engaged, thoughtful kids!"
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A Developer's Area column on Java for those coming from a teaching background who seek programming advice and those with a software development background who seek to develop an item of value to the teaching and learning communities.
This simple Javascript-enhanced web page leads students on an exploration of the "Josephus Problem," a classic problem of recreational mathematics involving the elimination of people arranged in a circle.
This Flash Forum tutorial not only discusses the programming involved in rendering simple polyhedra in Flash CS3, but it also gives an elementary discussion of the mathematics behind 3D rendering on a 2D computer screen.
This paper describes a Flash-based OSSLET that we have used at the United States Military Academy with first year calculus students as a vehicle for motivating vectors, matrices, and linear and affine transformations.
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Past Years Schools Exam Papers...
- increase students' exposure to a wide variety of questions from various schools;
- allow students to see the trend & type of questions favourable in the O Levels Exams;
- eventually able to boost confidence through continual practices.
Exam Buddy
Exam Buddy is a Mathematics Note Book written specially in students' lingo.
It contains . . .
- important formulae,
- easy-to-understand problem solving methods,
- hightlights routine exam questions,
- and higher order (challenging) questions that were recently seen in the exams.
Exam Buddy focus on students' weaknesses and provides detailed explanation of methods used in problem solving.
Exam buddy contains examples that are lined up in order of progressive difficulty so that students can learn in a progressive manner from the basic questions to the challenging ones. Examples given in Exam Buddy were selected from questions that are commonly seen in recent years exam papers reviewed from over 100 top and neighbourhood schools in Singapore.
Exam Buddy makes learning of Mathematics easy & ineresting!
The Practice Book is a compilation of exam questions selected from over 100 top and neighbourhood schools in Singapore.
It contains a series of practice questions from the basic, to the advance and to the most challenging questions often seen in school exams and tests.
NOTE:
It is compulsory for students in Teach Me Math (Tuition Class) to purchase and use Exam Buddy.
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More About
This Textbook
Overview
This text is an unbound, binder-ready edition.
Sheldon Axler's Precalculus focuses only on topics that studentsactually need to succeed in calculus. Because of this, Precalculusis a very manageable size even though it includes a studentsolutions manual. The book is geared towards courses withintermediate algebra prerequisites and it does not assume thatstudents remember any trigonometry. It covers topics such asinverse functions, logarithms, half-life and exponential growth,area, e, the exponential function, the natural logarithm andtrigonometry. The Student Solutions Manual is integrated atthe end of every section. The proximity of the solutions encouragesstudents to go back and read the main text as they are workingthrough the problems and exercises. The inclusion of the manualalso saves students money. Axler's Precalculus is availablewith WileyPLUS, a research-based, online environment for effectiveteaching and
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Includes 612 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. In this title, you will have access to 25 detailed videos featuring Math instructors who explain...
Addresses a focused theme on mathematics education. This title intends to illustrate the diversity within the theme and the research that translates into classroom pedagogies. It illuminates how application
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Fourier Analysis
Publisher:
John Wiley
Number of Pages:
488
Price:
94.95
ISBN:
0-471-66984-9
This is a good Fourier analysis textbook for upper level undergraduates and for lower level graduate students. The numerous applications in the book make it appealing to engineers and both applied and pure mathematicians who feel the need to justify their existence.
The topics included in the book are quite extensive, including boundary value problems, spaces, Sturm-Liouville problems, convolution and the delta function, Fourier transforms and integrals, and special topics such as DFT, FFT, and filtering, and wavelets. This book certainly has plenty of material for a two semester sequence in Fourier analysis.
Stade incorporates tidbits about the history of Fourier analysis throughout the text by not only including when people studied the material but also why they were interested in it. This gives the subject some context and perspective that is quite refreshing to see in a mathematics textbook — so often the historical material is only incorporated in lower level textbooks.
Throughout the text, Stade uses DIY (Do It Yourself) to indicate places where he has skipped steps to get a result. Although this phrase will not necessarily be popular among students, it is less pompous than statements like "it can easily be shown," which students tend to find frustrating when they can't "easily see it." In addition, he has included plenty of examples throughout the text and often refers to them in the exercises. The exercises are very straightforward and sometimes even include hints, which will certainly be popular with students.
The author does a great job of incorporating his sense of humor throughout this book. (He has given a talk entitled "Joseph Fourier and the Birth of Disco" several times. Although no mention of disco is made in this text, Jimi Hendrix does make an appearance.) This makes the book more enjoyable. As faculty we often complain that the students don't read their books, but then we often supply them with dry material. Stade went to great lengths to include humor—even poking fun at himself:
Evaluation of infinite series is a sport enjoyed by many people. Number theorists, of whom the author is one (as he will admit freely in most social situations), are especially keen on this sport, because of the relevance of these series to the behavior of prime numbers and to other, more or less (or much less) related, phenomena. Others take part because infinite series and their values have applications in chemistry, in physics, and so on. But like all sports, the primary and best reason for participating is just for fun. (If anyone knows how to have fun, it's the number theorists, we can assure you.)
Sharon Schaffer Vestal is Associate Professor of Mathematics at Missouri Western State University in Saint Joseph, Missouri.
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Washington MESA
Washington MESA (Mathematics, Engineering and Science Achievement) is developing middle and high school curriculum units and middle school modules/books available through Cuisenaire Dale Seymour Publications that integrate concepts within mathematics
...more>>
WebGrapher - Tom Cooper
This page contains a graphing applet that can be used online or downloaded.
The applet can create dynamic graphs with sliders that can be saved as web
pages. Users can plot points, functions, parametric functions, polygons,
vectors and more. There
...more>>
What kind of math? Photo Challenge - Kathryn Mann
Pictures of math graduate students with word-bubbles showing "the kind of math that's right" for them. Submit your own group snapshots and subfields. Inspired by an observation that a flyer from the American Mathematical Society (AMS) reinforced sexist
...more>>
Zentralblatt MATH Database - Springer-Verlag
A database edited by the European Mathematical Society, the FIZ Karlsruhe, and the Heidelberg Academy of Sciences, and established in cooperation with Math Doc Cell (France). Search for abstracts of papers on any math subject by author, title, classification,
...more>>
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7.
AIM Design AIM is both relevant and rigorous. AIM is relevant because students can see how math applies as they build robots to meet challenges. AIM is relevant because it can lead to high-tech jobs. AIM is specifically designed with the rigor associated with pre-calculus or statistics classes. Exploratory learning is combined with Accuplacer-like weekly tests that demand mastery of the content.
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More About
This Textbook
Overview
"I love math!" "I hate math!" Whether you're a math aficionado or someone who cringes at calculations, Paramedic: Calculations for Medication Administration will make you a master of paramedic math.
This textbook teaches the basic principles of mathematics and applies these principles to cases that paramedics face on the job. Chapters cover math rules and principles; fractions, decimals, and percentages; ratios, proportions, and conversion factors; and rate-dependent and weight-based calculations.
Practice problems are scattered throughout the chapters; students practice as they go. Every chapter highlights how paramedics can make use of the math knowledge that they already have in order to solve more complicated problems. Chapters begin with the simple and obvious, and progress to the level used in the field.
Practice makes perfect—this text has over 700 practice problems! In addition to the in-chapter practice, chapters conclude with more problems. Complete answers to every problem, including explanations, are provided in the answer key. Every step is included, making it easy to follow how an answer was reached
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Descriptions and Ratings (1)
Divided into the following sections:
Basics
Constructing a few simple matrices
Portions of matrices and vectors
Defining/changing variables
Plotting
Arithmetic and functions of numbers
Arithmetic and functions of vectors and matrices
Solving linear equations
Transposes and dot products
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...
Show More illustrate several mathematical methods that are essential in successfully solving process engineering problems. The book first provides an introduction to differential equations that are common to chemical engineering, followed by examples of first-order and linear second-order ordinary differential equations (ODEs). Later chapters examine SturmLiouville problems, Fourier series, integrals, linear partial differential equations (PDEs), and regular perturbation. The author also focuses on examples of PDE applications as they relate to the various conservation laws practiced in chemical engineering. The book concludes with discussions of dimensional analysis and the scaling of boundary value problems and presents selected numerical methods and available software packages. New to the Second Edition Two popular approaches to model development: shell balance and conservation law balance One-dimensional rod model and a planar model of heat conduction in one direction Systems of first-order ODEs Numerical method of lines, using MATLAB® and Mathematica where appropriate This invaluable resource provides a crucial introduction to mathematical methods for engineering and helps in choosing a suitable software package for computer-based algebraic applications
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There's no such thing as too much practice. This reproducible program builds skills incrementally. By inviting students to "show what they know" in a variety of new formats, these stimulating lessons will enable struggling students to actually enjoy the learing process. As in all of the binder programs, the dual emphasis is on (1) mastery of the basics... more...
Meyer's Geometry and Its Applications, Second Edition , combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text... more...
Say,...Deformable objects are ubiquitous in the world, on various levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. This book provides an overview of the state of science in analysis and synthesis of non-rigid shapes. more...
Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more...
The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... more...
egghead's Guide to Geometry will help students improve their understanding of the fundamental concepts of geometry. With the help of Peterson's new character, egghead, students can strengthen their math skills with narrative cartoons and graphics. Along the way there are plenty of study tips and exercises, making this the perfect guide for students... more...
The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies... more...
This book mainly deals with the Bochner–Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner–Riesz means and important achievements attained in the last 50 years. For the Bochner–Riesz means of multiple Fourier integral, it... more...
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Course Description
This course will introduce students to various applied technical math concepts required to analyze and study topics of the industrial maintenance field. Topics will include fractions, measurement, algebra, geometry, trigonometry, graphs, and statistics. Topics are presented at the introductory level with an emphasis on applications.
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books.google.com - Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently... Algebraic Curves
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Abstract
As graphics calculators are mainly devices for student learning, it is important that curricula and examinations are constructed to incorporate them in a coherent way. Three recent developments in graphics calculators are described and analysed to determine their implications for examinations. Symbolic manipulation on algebraic calculators challenges existing emphases in many examinations and their associated curricula. Flash memory allows calculators to be efficiently upgraded, but threatens the equity of students with different calculators or even the same calculator with different capabilities. Developments in memory storage increase the possibilities of students having access to significant text storage during examinations. Suggestions are made for ways of incorporating these developments into mathematics education in equitable and beneficial ways.
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Editor's Pick
Fresh Articles
Mathematical Models H M Cundy and A P Rollett
This book, which by now must be regarded as a classic, encourages the student (or teacher) to get pencil, paper, scissors and glue to explore Mathematics in a practical way.
The section on models in plane geometry contains discussions on loci and...
Mathematics is a fascinating subject which teaches students to think clearly and logically. It is impossible to be a 'woolly thinker' in Maths, which is one of the reasons it is highly prized as a qualification.
In our present age, where emotions and self-expression are often prioritised, it...
Orphaned orangutans needed to improve their climbing skills – could students design a way to get them back to their swinging best?
Some of the world's most intelligent and emotional primates, orangutans are more similar to humans than some people would like to think.Yet despite this, humans are...
The EDEXCEL A-level mathematics course produces a series of books with a style I can recommend. The subject is presented in a logical manner with clarity and a number of different styles of question on each topic, well annotated.
Authors L.Bostock and S.Chandler have produced classic books for...
What is a limit?
When a person reaches his or her limit then they can say all I can do is this much and can quantify the amount they can do. Well, in maths it is the same scenario.
Certain functions which are 'told' to keep going or x----->infinity. f(x) or y will reach a limit.
This is true...
Top Tip for Top Grade
I meet many students who feel satisfied when they understand a mathematical concept, and feel no need to practise further.
Though it's important to understand concepts for relevance, problem-solving and a foundation for further understanding, for a top grade in exams it...
One of my favourite areas of mathematics is probability, and this question is an example of why I love it so much. The answer is counter-intuitive - what do you think it is?
In this question you can assume that the probability of giving birth to a boy or girl are equally likely. The question...
Perhaps the first question should be, "Why would you want maths?" Well, in order to answer that, we have to realise what maths is. For many people, maths goes something like this:
"Here are some meaningless symbols. If this bunch of symbols looks like that bunch of symbols, do such and such and...
Doing Mathematics at A-Level opens the door to a wide range of careers, including medicine, business, computing, geophysics, biosciences, construction and even Formula 1.
It is one of the hardest subjects and doing well in it reflects your high intellectual abilities. Many subjects at...
A teacher should have a lot of qualities but most of the qualities mentioned here are those which a good teacher must possess.
1-Command Of The Subject
A teacher must have command of the subject with up-to-date knowledge, particularly of the topic in discussion in any lesson to be delivered so...
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Book Search
Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in "Matrix...
Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number...
Published August 5
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Geometry of Design Studies in Proportion and Composition
9781568982496
ISBN:
1568982496
Pub Date: 2001 Publisher: Chronicle Books Llc
Summary: What Do a Pine Cone, A Trout, and the Human Body Have in Common? They all have natural proportioning systems that provide the foundation for the work of many-some would say all-artists and designers. Revealing these natural systems, Kimberly Elam uncovers the mysterious relationship between mathematics and beauty. She takes us into the magical realm of geometry-of Golden Sections and Divine Proportion and the Fibonac...ci Sequence-in language accessible to the most math-squeamish. From there, Elam shows us how symmetry, order, and visual balance underlie designs from the posters of Jan Tschichold to Mies's Barcelona Chair to the new Volkswagen Beetle.
Elam, Kimberly is the author of Geometry of Design Studies in Proportion and Composition, published 2001 under ISBN 9781568982496 and 1568982496. Eight Geometry of Design Studies in Proportion and Composition textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $2.64, or buy new starting at $10.95.[read more]
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Description
For shorter courses in business mathematics, personal finance, or small business management that are typically taught in either the first two years of college or the last two years of high school.
This text brings together core math tools students need to successfully handle everyday business transactions, manage their personal finances, and run a small business. Throughout, students learn math in familiar contexts they already care about. Conversational, easy to read, and exceptionally accessible, this text combines depth and breadth with practical examples and clear step-by-step instructions — all delivered flexibly to support multiple modes of teaching and learning. This edition contains extensive new coverage of wealth building through investment; the latest credit trends, and more. It is accompanied by an expanded collection of interactive online learning and teaching resources unparalleled in its market, including Pearson's newly-revamped MyMathLab.
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2004 HardcoverFlorence, Kentucky, U.S.A. 2004 Hardcover 5th or later Edition As New Book 7 th edition. The book looks like new, unread and clean. Edges are sharp and fine. No tears or ...creases. No stain, writing or reminder marks. The binding is straight and tight. Comes with sealed CD-ROM. Standard shipping is by USPS Media Mail & Expedited shipping is by USPS Priority Mail or equivalent.Read moreShow Less
More About
This Textbook
Overview
Tried and true, Gustafson and Frisk's ALGEBRA FOR COLLEGE STUDENTS teaches solid mathematical skills while supporting the student with careful pedagogy. Each book in this series maintains the authors' proven style through clear, no-nonsense explanations, as well as the mathematical accuracy and rigor that only Gustafson and Frisk can deliver. The text's clearly useful applications emphasize problem solving to effectively develop the skills students need for future mathematics courses, such as college algebra, and for real life. The Seventh Edition of ALGEBRA FOR COLLEGE STUDENTS also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes BCA/iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by BCA/iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math.
Related Subjects
Meet the Author
R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois University.
Peter D. Frisk, Professor Emeritus of Mathematics at Rock Valley College, earned both a Bachelor of Arts and a Master of Arts in mathematics from University of Illinois. He is the coauthor of several best-selling math texts including BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, ALGEBRA FOR COLLEGE STUDENTS, and COLLEGE ALGEBRA. He has been the recipient of the Rock Valley Teacher of the Year
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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...Discrete mathematics includes a wide variety of topics relating to mathematics of discrete values, as opposed to continuous values. These include, but are not limited to combinatorics, set theory, probability, number theory and Diophantine equations, and graph theory. There are various applications in algebra geometry and calculus, and I can assist with these
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This course straddles the contentious divide between reform and tradition in calculus. It's goal is to mold biology majors into better scientists by enabling them to use Mathematica wisely, but it's approach embodies a firm conviction that skill in using high technology for complex procedures requires skill in using low technology (e.g., pencil and paper) for simple procedures. So it's outlook is thoroughly modern. But it's style is deliberately old-fashioned.
Materials
Lectures and course notebooks posted on the web
Description
Biocalculus introduces the fundamental ideas of calculus from the perspective of a biologist, i.e., it uses biological data to motivate and elucidate concepts that are essential for constructive use of Mathematica in solving biological problems. The approach is heuristic, but systematic. One can develop a great deal of mathematical maturity with remarkably little exposure to mathematical rigor, and these lectures encourage students to develop as much as possible of the first with as little exposure as possible to the second.
Topics:
Ordinary functions: an algebraic perspective
Smoothness and concavity: a graphical perspective
Quotients, inverses and limits. Modelling photosynthesis
Ordinary sequences. Fibonacci's rapid rabbits
Discrete probability distributions. Sums of powers of integers
Function sequences. Compositions. The exponential and logarithm
Index functions. Area and signed area
From index function to ordinary function: ventricular recharge
Area as limit of a function sequence. D'Arcy Thompson's mini minnows
Arterial discharge: the area under a polynomial
From ventricular inflow to volume: integration
From ventricular volume to inflow: the derivative as growth rate
Smoothness and concavity: an algebraic perspective
Making joins smooth: the derivative of a piecewise-smooth function
Differential notation. The derivative of a sum or multiple
Sex allocation and the product rule
How flat must a flatworm be, not to have a heart? The fundamental theorem
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Mathematics (MATH)
Mathematics has long been the basic language of the natural sciences, and has been studied for its own sake since ancient times. An understanding of the basics of calculus, statistics, and linear algebra has become a requirement for proficiency in many of the social sciences. The study of mathematics has its own rewards because accomplishment in the subject, even at a relatively elementary level, requires and promotes clarity of both thought and expression. For many, the study of mathematics offers entrance into an exciting world of challenges where beauty and utility coexist in balanced harmony.
A major in mathematics may be seen as the first step toward obtaining a graduate degree in one of the mathematical sciences, or it may constitute preparation for a professional degree program in a field such as education, medicine, law, or business. It also opens the door to a whole range of employment opportunities, as the analytical skills that a student develops in pursuing a major in mathematics are greatly valued by potential employers. There are, for example, excellent career prospects in actuarial work and in the rapidly growing areas of biomathematics and biostatistics (interpreting results of clinical trials), modeling (in industry, government, and finance) and cryptology (in banking, television, the Internet, and elsewhere).
Secondary Teacher Certification
Prospective secondary school teachers (grades 7 – 12) must complete one of the three majors within the department. This certification requires specific mathematics and education courses. Students seeking teacher certification should confer as early as possible with the mathematics and education departments to devise a program of study, which normally will include all requirements for certification in the Commonwealth of Pennsylvania.
Departmental Honors
Students who complete departmental honors normally have a grade point average of 3.5 both in their mathematics courses and overall. Students in the Bachelor of Arts in Mathematics major or Bachelor of Science in Mathematics major have usually completed MATH 308 Real Analysis I and MATH 320 Abstract Algebra I by the end of their junior year. Students in the Bachelor of Science in Applied Mathematical Sciences major have usually completed MATH 308 Real Analysis I by the end of their junior year. To be accepted into the Honors Program, a student must submit an honors proposal for approval by the adviser, the department chairperson, and the Honors Council. The student must then complete an honors thesis under the adviser's direction, must have completed a total of at least three mathematics courses at the 300- or 400-level by the end of their junior year, and satisfy all other requirements as put forth by the University Honors Council. Such students usually complete at least two half-credit semesters of independent study in mathematics (MATH 491 Reading and Research).
Mathematics Majors
The Mathematics Department offers three majors. Students may earn a Bachelor of Arts in Mathematics, a Bachelor of Science in Mathematics, or a Bachelor of Science in Applied Mathematical Sciences. Students in each major complete an introductory year of calculus either by taking MATH 201 Calculus I or MATH 202 Calculus II during their first year, or by achieving a high score on the Advanced Placement Test of the College Entrance Examination Board.
The College Core Curriculum disciplinary depth requirements for Bachelor of Science and Bachelor of Arts majors are satisfied as follows:
The requirement for a Culminating Experience within the major may be satisfied in any of the following ways:(1) taking a full credit 400-level mathematics course; or (2) completing an honors thesis, senior thesis, or other research project in the senior year that involves mathematics or statistics; or (3) completing student teaching for secondary certification. The Culminating Experience cannot double-count as one of the mathematics electives required in the major, with the one exception that students earning a Bachelor of Arts in Mathematics may count a 400-level mathematics course both as their mathematics-related course and as the Culminating Experience.
The choice of degree program depends largely upon the student's mathematical objectives and interests in fields other than mathematics. Students with strong interests outside mathematics have options including the Bachelor of Science in Applied Mathematical Sciences program, the Bachelor of Science in Interdisciplinary Studies in Economics and Mathematics program, and the Bachelor of Arts in Mathematics program. Students with a strong interest in a career in mathematics or science – and in particular, students planning to continue on to Ph.D. programs in the mathematical sciences – are strongly advised to take courses beyond the minimum requirements for the major. Since a maximum of 12 courses in any one department may be counted toward any Bachelor of Arts degree, such students are advised to choose one of the Bachelor of Science majors.
Bachelor of Arts in Mathematics
The Bachelor of Arts in Mathematics major consists of eight mathematics courses beyond the introductory year of calculus, plus one additional course in a related field and a Culminating Experience.
Of the eight mathematics courses beyond the introductory year of calculus, five are specified:
Additional full-credit computer science or science course (beyond those required for all liberal arts students) in which college-level mathematics or statistics plays a major role. Included among the courses are nearly all courses in computer science or physics at or above the 200 level and an appropriate course from the humanities, social sciences, or engineering in which mathematics plays a significant role at a reasonable level of sophistication.
The mathematics department chair shall make the determination of whether or not a particular course outside the mathematics department may count as the course in a related field.
A single 400-level course may be used to satisfy both the Culminating Experience requirement and the related course requirement.
Students with a special interest in pure mathematics or statistics can earn formal concentration in these areas by completing an appropriate suite of 300- and 400-level courses, as described below.
The additional laboratory science courses may be chosen from any discipline in the natural sciences or from computer science. Any course in physics beyond PHYS 212 Classical and Modern Physics, and any laboratory course in computer science at the level of CSCI 203 Introduction to Computer Science I or beyond, may be chosen.
Students with a special interest in pure mathematics or statistics can earn formal concentration in these areas by completing an appropriate suite of 300 and 400-level courses, as described below. In particular, those intending to pursue graduate study in mathematics or statistics should plan to complete the relevant concentration.
Students majoring in mathematics with a special interest in computer science are encouraged to consider minoring in computer science.
Bachelor of Science in Applied Mathematical Sciences
The Bachelor of Science in Applied Mathematical Sciences major (with a concentration in statistics or applied mathematics) requires 10 mathematics courses beyond the introductory year of calculus, a computing course, five courses in a different program, and a Culminating Experience. More specifically, there are six required core mathematics courses consisting of:
Four concentration related courses in statistics or applied mathematics
4
Further, the major requires a computing course and significant coursework in a declared outside department or program as described below. While the Culminating Experience may be met in any of the ways specified above, students earning a Bachelor of Science in Applied Mathematical Sciences are strongly encouraged to consider the option of a thesis or research experience integrating the outside coursework.
Appropriate courses could be additional electives counting toward the concentration if so determined by the academic adviser in consultation with the mathematics department chair.
The computing course can be a computer science course at or above the 200-level or a computing course appropriate to the program of study as determined through consultation with the academic adviser and the mathematics department chair.
Outside Coursework
For the purpose of completing a coherent sequence of courses that provide a solid introduction to the discipline all students must partner with a department or program in a discipline that applies statistics or mathematics. In this regard, a minimum of five courses chosen in consultation with the Mathematics Department adviser and the outside department or program is required. A partner department/program will usually be chosen from the College of Engineering, the School of Management, the Division of Social Sciences, or the Division of Natural Sciences. Entering students can declare the intended major in the summer after acceptance to Bucknell, but must consult with the Mathematics Department and formally declare the outside coursework by the end of their third semester. All other students must consult with the Mathematics Department at the point of declaring the major and specify the outside coursework. In either case the Mathematics Department will consult with the partner department or program to ensure that the coursework is appropriate and can be completed.
A sample sequence for the Bachelor of Science in Applied Mathematical Sciences major is provided below. It should be noted that each student's sequence will be unique, depending on when the program is started, how many AP or transfer credits are applied, and when the desired courses are offered.
Courses
MATH 112. Introduction to Mathematical Modeling. 1 Credit.
Offered Spring Semester Only; Lecture hours:3 Introduction for the non-specialist to mathematical modeling of real-world phenomena such as voting and networks, using graph theory, probability, and other accessible tools.
MATH 117. Introduction to Mathematical Thought. 1 Credit.
Offered Spring Semester Only; Lecture hours:3,Other:1.5 An investigation of number, numeration, and operations from the perspective of elementary school teachers and pupils. Open only to B.S. in Education Early Childhood Pre-K to 4 students. Required fieldwork.
MATH 118. Elementary Geometry and Statistics. 1 Credit.
Offered Fall Semester Only; Lecture hours:3 Investigation of geometric, probabilistic, and statistical concepts related to Pre-K to 4 mathematics and how children learn and make sense of these concepts. Prerequisite: permission of the instructor. Prerequisite: MATH 117 or permission of the instructor.
MATH 192. Topics in Calculus. 1 Credit.
Offered Spring Semester Only; Lecture hours:3 Elementary calculus and applications taken primarily from economics. Topics include algebraic, exponential, and logarithmic functions, graphs, limits, derivatives and integration. Not open to students who have taken MATH 201.
MATH 201. Calculus I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:4 An introduction to the calculus of algebraic, trigonometric and transcendental functions. Interpretation, significance and calculations of a derivative. Applications to geometry, biology, physics, economics, and other subjects. Introduction to the definite integral, including the Fundamental Theorem of Calculus. Not open to students who have taken MATH 192.
Offered Fall Semester Only; Lecture hours:Varies; Repeatable Mathematical problem solving, with an emphasis on problems and topics that appear in contests such as the Putnam Competition. Prerequisite: permission of the instructor.
Offered Both Fall and Spring; Lecture hours:3 Basic methods of solving ordinary differential equations. Systems of linear differential equations, Laplace transform, applications and selected topics. Prerequisite: MATH 211. Not open to students who have taken MATH 222.
MATH 216. Statistics I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3,Other:1 Exploratory data analysis, sampling distributions, regression, sampling designs, confidence intervals, hypothesis testing, ANOVA. Statistical software is used and applications, including projects, are undertaken. Not open to students who have taken MATH 226 or PSYC 215.
Offered Spring Semester Only; Lecture hours:2 First order differential equations, second order linear equations, higher order linear equations, numerical approximations. Prerequisite: MATH 211. Open only to civil engineering and computer science engineering students. Not open to students who have taken MATH 212.
MATH 226. Probability and Statistics for Engineers. .5 Credits.
Offered Fall Semester Only; Lecture hours:2 Descriptive modeling and statistics, sampling and experimental design, discrete and continuous random variables, central limit theorem, and elementary inference. Prerequisite: MATH 202. Open only to engineering students and students in computer science. Not open to students who have taken MATH 216.
Offered Either Fall or Spring; Lecture hours:Varies; Repeatable Readings and research in special topics at an intermediate level. Prerequisites: permission of the instructor, adviser, and department chair.
Offered Both Fall and Spring; Lecture hours:3 Real numbers and elementary topology of Cartesian spaces, convergence, continuity, differentiation, and history of the development of analysis. Prerequisites: MATH 211, MATH 245, and MATH 280.
MATH 311. Theory of Numbers. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3 Classical number theory in an algebraic setting. Topics include unique factorization, diophantine equations, and linear and quadratic congruencies. Advanced topics from algebraic or analytic number theory. Prerequisites: MATH 245 and MATH 280, or permission of the instructor.
Offered Both Fall and Spring; Lecture hours:3 Groups and rings; homomorphisms and isomorphism theorems; history of the development of algebra. Additional selected topics. Prerequisites: MATH 245 and MATH 280.
Offered Either Fall or Spring; Lecture hours:2; Repeatable Seminar based on topics from algebra, analysis, topology, differential equations, statistics, or applied mathematics; topics selected according to demand or interest. Prerequisite: permission of the instructor.
MATH 391MATH 392Offered Either Fall or Spring; Lecture hours:3 Topics in statistics and mathematics. This course is designed for seniors to satisfy the Culminating Experience requirement. Prerequisites: MATH 280 and a 300-level mathematics course or permission of the instructor
MATH 492. Reading and Research. .5-2 Credits
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About This Course
This course covers topics such as functions, exponentials, linear equations and parabolas. The math instructors are experienced and knowledgeable educators who have put together comprehensive video lessons in categories ranging from how to use FOIL to factors to trigonometry.
Each category is broken down into smaller chapters that will cover topics more in-depth. These video lessons make learning fun and interesting. You get the aid of self-graded quizzes and practice tests to allow you to gauge how much you have learned.
Course Topics
Category
Objectives
Functions
Learn about transformations, domain, range and inverse functions. Also learn how to compose functions, evaluate composite functions and manipulate functions.
Evaluating Exponential and Logarithmic Functions
Learn about exponential functions and logarithms. Take a look at graphing, evaluating and solving equations with exponential functions and logarithms.
Find out about the different types of numbers, parts of a graph, linear equations and system of equations. Study intercepts, standard form and graphing.
Graphing and Rational Equations
Learn how to graph reflections across axes, the origin and line Y=X. Practice solving rational equations and finding the least common denominator.
Factoring and Graphing Quadratic Equations
Study parabolas and learn to multiply binomials and factor quadratic equations using FOIL. Also take a look at completing the square.
Exponents and Polynomials
Study exponent properties and discover how to define a zero and negative exponent, simplify expressions and use rational exponents. Additionally, learn about working with polynomials, graphing cubics and using long and synthetic division on polynomials.
Piecewise and Composite Functions
Examine piecewise functions and learn how to graph them.
Geometry and Trigonometry
Learn how to solve visualizing geometry problems, calculate the volumes of basic shapes and use the Pythagorean Theorem.
Using Scientific Calculators
Explore how to use a scientific calculator to work with radians, degrees, trigonometry functions and graphs.
Trigonometry
Learn to graph sine, cosine and transformations. Also, study right triangles and the double angle formula and learn to solve trigonometry equations
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Synopses & Reviews
Publisher Comments:
The must-have solution for every parent and teacher struggling with the new Common Core math standards that their middle-school students must know to succeed
Nearly half of adults, including parents of middle-school students, have never heard of the Common Core State Standards, let alone have a working knowledge of what exactly their children face when it comes to middle-school math. Even teachers acknowledge struggling with how best to teach their students these math standards.
CliffsNotes comes to the rescue with this Grade 8 Common Core Math Review. Aligned to the state standards, this book provides essential coverage of the Grade 8 CCSS math that's challenging middle-school students, teachers, and parents alike.
The material covers all of the math standards that comprise Grade 8 CCSS math:
• The number system
• Geometry
• Expressions and equations
• Functions
• Statistics and probability
Two practice tests round out the book, plus every review chapter includes example problems.
Synopsis:
This 3rd Edition of CliffsNotes FTCE Professional Education Test encapsulates the major test changes to this important Florida teacher certification test that would-be Florida teachers must pass to become credentialed.
Synopsis:Synopsis:
A review of the topics that comprise Grade 8 Common Core Math, including subject reviews, example problems throughout, and two practice tests.
Synopsis:
A subject review of the Common Core Math for Grade 6, including topic reviews, example problems, and two practice tests to help students better understand this high-stakes subject.
Synopsis:
Synopsis:
About the Author
Dr. Sandra Luna McCune is Regents Professor in the department of elementary education at Stephen F. Austin State University in Texas. Dr. E. Donice McCune is Regents Professor of Mathematics at Stephen F. Austin State University.
This 3rd Edition of CliffsNotes FTCE Professional Education Test encapsulates the major test changes to this important Florida teacher certification test that would-be Florida teachers must pass to become credentialed.
"Synopsis"
by Firebrand,"Synopsis"
by Firebrand,
A review of the topics that comprise Grade 8 Common Core Math, including subject reviews, example problems throughout, and two practice tests.
"Synopsis"
by Firebrand,
A subject review of the Common Core Math for Grade 6, including topic reviews, example problems, and two practice tests to help students better understand this high-stakes subject.
"Synopsis"
by Firebrand,"Synopsis"
by Firebrand,
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You could have multiple choice questions, or you could use pattern matching with alternatives that you would hope would catch the acceptable answers.
But why not, in this day and age, give students something better? Why not have the students write short mathematical essays in notebook form on various topics where they might explain how they got an answer and the principles behind it? Of course, that means the teacher would have to actually read the notebooks, and the student would also have to learn how to write readable and clear presentations.
I'm building a little Mathematica system that checks answers entered by students. Suppose the question is "what is Sin'[x]?" ad the student responds: Sin'[x] which is "correct", but not the intended answer (Cos[x]). I'm wondering if there is a general way to approach this sort of problem. In particular, is there a way to find out whether a given expression includes certain elements (like Derivative)?
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... Enjoy the Bridge Project's high quality graphics and physics while putting your most spectacular bridges to the test. Download free levels from the global bridge builder community, and participate in ...
Solutions to dozens of basic formulas from physics, technology and mechanical engineering. Help, pictures as well as many selection tables with values of various coefficients and material properties are available ...
... of bird song or a multimedia presentation of physics experiment can drastically increase students' understanding of the process and make it easier to remember the material. Plus, teachers and professors ...
... utility for students, teachers, and practitioners in engineering, physics, sciences, and technical subjects. It can quickly convert more than 1500 different units in 78 categories. It contains the most important ...
... divided into such categories as Mathematics, Chemistry, Biology, Physics, Engineering and Computing. Icons are carefully created pixel by pixel by the hand of a professional artist. They shine with a ...
... understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus. Microsoft Mathematics includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional ...
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Algebra 2 eTextbook & Printed ST (2nd ed.)
This item includes a copy of the printed Student Text as well as a VitalSource eTextbook.
Algebra 2 Student Text (2nd ed.) focuses on developing thinking and reasoning skills through the discussions of algebra concepts such as quadratic equations, polynomials, complex numbers, and trigonometry. Relevant applications and examples are presented in the feature sections "Algebra and Scripture" and "Algebra Around the World." Reference tables and a glossary of algebra terms are included in the back of the book.
Includes 284182 eTextbook and 267781 printed Textbook.
This eTextbook is offered through the VitalSource Bookshelf platform. Delivering digital content to more than 1.6 million users on 6,000 campuses in 180 countries. VitalSource® is the preferred and most used eTextbook platform in higher education today.
Features of VitalSource® eTextbooks:
Simple process—After the book is purchased, the student signs up for a free Vitalsource Bookshelf account online, enters the special code received from BJU Press, and receives the eTextbook in his virtual bookshelf.
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Introduction to Excel Part Two: Formatting an Existing. Spreadsheet. Purpose.
Upon completion of this tutorial you will have learned how to format the following:
.the stern of the ship. By flooding the deck the ship can lower itself and ... For example was the hydrostatics of the craft evaluated many times during the ..... Using the volume of the platform when it is lowered the draught of the craft can ..... theory. It is concluded that this is not the optimal tool for this ...
Source:
Mathematics for Computer Scientists. 5. Introduction. Introduction. The aim of this
book is to present some the basic mathematics that is needed by computer ...
Source:
Mathematics for Computer Scientists. 5. Introduction. Introduction. The aim of this
book is to present some the basic mathematics that is needed by computer ...
Source:
The rationale of teaching Basic mathematics is that it plays the role of filling up ..... All of the readings for the module come from Open Source text books. This.
Source:
mathematics, the standard mathematical methods and notations of the past. .....
The Mathematical Century: The 30 Greatest Problems of the Last 100 Years,.
Source:
1. Microsoft Outlook 2010: Working with Quick Parts. An Outlook email Quick Part
is a block of text that you can insert in an email message. You can use Quick ...
Source:
Outlook 2007's Quick Parts. Use the Quick Parts feature to save snippets of both
text and images for easy reuse and avoid entering the same things into email ...
Source:
This book aims to be a shortcut to graphics theory and programming in JOGL. ...
JOGL and Java3D sample programs (their sources and executables) are ...
Source:
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Recommended Supplement:The student solutions manual contains worked out solutions for all even
problems in the textbook.The
solutions manual for our textbook has ISBN 0495012343.Stewart has written several different
calculus textbooks, each of which appears in several different editions, so
please check the ISBN before making a purchase. Copies of the solution manual
will be available at the Reserve Readings collection in Collier Science Library
(not there quite yet)
Learn
that mathematics can be used to study real world situations. This process
is called mathematical modeling. In our course it will involve using
functions and their derivatives and integrals .
Learn
how to work with various representations of functions (graphical, tables,
formulas) and become proficient in using certain types of functions (linear,
quadratic, polynomial, trigonometric, exponential and logarithmic).
Understand
how the area under a curve can be approximated by adding up boxes and that
the limit of this procedure leads to the integral.
Understand
how derivatives and integrals are related via the Fundamental Theorem of
Calculus.
Learn
how to compute integrals both for simple functions and for more
complicated functions.
Learn
the meaning of an integral in a variety of applications.
Learn
how to add up infinitely many numbers (a series) and then add up
infinitely many functions.
How
to use simple functions to approximate complicated functions (Taylor
approximations, Taylor Series).
Use
the computer system Mathematica to do
computations related to the above topics and to plot curves.
Process Goals of the Course:In this
course, you will
Find
connections between the mathematics we are studying and real world
situations.
Communicate
your mathematical reasoning in writing and verbally.
Develop
your ability to work as an independent and self-sufficient learner by
facing the challenge of "What to do when you do not know what to do".
How
to take what you have learned in one situation and apply it to a new and
different situation (transfer of knowledge)
Get
comfortable with not knowing the answer immediately
Learn
material we have not covered in class by reading the book and applying
this newly learned information to solve problems.
Become
part of a community of learners who support, encourage and learn from one
another.
We will cover the following material
from Stewart. Sections in () indicate material that will be covered briefly or
might be omitted.
Ch.5:
Section 5
Ch.
6: Section 1, 2, (3), 4, 5
Ch.
7: Section 1, 2, 3, 4, 5, 6, 8.
Ch.
8: Section 1, 2, 3, (4), 5, 6, 7, 8
Ch.
9: Section 1, 2, 3, 4,
Ch.
12: Section 1, 2, 3, 4, 5, 6, 8, 9, 10, 11
Other material might be included as
time permits.
Learning Theory:
A common misconception in the United
States is that only a gifted few people can do mathematics successfully; "you
either have it (the ability to mathematics) or youdon't".The reality, as demonstrated by
educational studies of student learning, is that the majority oflearners can
reach a reasonable level of mathematical competency providing they work hard at
it. Another misconception is that one's intellectual ability is fixed from a
young age onward. Research in neuroscience shows that people's brains continue
to develop throughout life; the brain makes 20,000 new neural connections per
day.Thus, by appropriate training,
one can actually "get smarter".
My goal is to have all students in this
course be successful in mathematics and to help you become smarter at the end
of the course than you were at the beginning. This will require hard work and
facing new challenges that will stretch your thinking. Learning new ideas and
becoming fluent in applying them takes time and can involves periods of
frustration. If you have this experience, do not worry; it is normal.
Course Components:
Classroom:
During class, there will be a mixture
of lecturing by the professor and time spent by the students working out
problems and discussing their results in groups. Research has shown that this
type of active participation, in which one explains one's reasoning as well as
thinks about others' explanations, leads to improved learning. Explaining your
reasoning requires a different and higher level of thinking skill than does
simply doing the problem.
The group work does not go well when
members of the group are absent. Therefore it is important that you attend class.
Please be respectful of your fellow students.
If you decide to take this course, you
must commit to attending class regularly.
Homework:
a. There will be homework related to
each class session coming from the textbook: practice problems and assigned
exercises.The assigned problems
will be collected once a week on Mondays. Even though the homework will only be
collected weekly, you should do part of the homework after each class.Out of respect for the time and effort
of the graders, late work will not be
accepted unless there is a special situation (ex. serious medical problem)
and you get my permission ahead of time.
b. To make the time we spend working in
groups most effective, you will have some short assignments that will need to
be completed by the following class period so that you can share your work with
your group.
The best way to learn mathematics is by
doing lots of problems. Do not limit yourself to just doing the assigned
problems that you are required to hand in. You should do some problems after
each class. This way, the next lecture will make a lot more sense. Do not wait
till the last minute and do all the problems at once. You will have much more
trouble understanding the lectures and will therefore be using your time
inefficiently.
To help you be aware of the time you
are spending on the homework and how your are distributing the time over the
course of the week, you will turn in a time logwith
each homework assignment which states the number of hours you spent studying
Calculus and working on the homework that week.
I encourage you to work together with
other students to solve the homework. However, the work you hand in must be
your own (i.e. you may not simply copy the answer from someone else).
Connections:
A major goal of the course is for you
to see how mathematics is related to things you are interested in. To this end,
we will have a "Connections" component to the course:
Over
the course of the semester, you will choose from the homework you are
assigned, two problems and for each one, write a short description (one
– two paragraphs), describing how the mathematics in the problem
could link to a real world situation. We will set up a forum on Blackboard
in which you will post these responses.
You
will look at other students' "connections" write ups, choose one that you
find interesting and write a short "reaction" to their post.
Final
Connections Project. You and a partner will chose one problem, from a list
I will give you, to explore independently. You will solve the mathematics
involved and write up your work clearly, demonstrating the mathematical
communication skills you have developed over the term. As part of your
write up, you will include a discussion of the problem. This project will
be due at the last class of the term.
Computer Component:Technology plays an increasingly important role in our world. To prepare
you to make use of the basic technology tools related to mathematics and the
sciences, you will learn the basics of the computer system Mathematica.
Many of you have used graphing calculators in high school. Mathematica
is a step up the technology ladder from graphing calculators.
To help you learn how to
use Mathematica, there will be regular computer-based
assignments. Math majors will be available in the Mathematics Computer Lab
(Park Sciences 354) at a variety of times to assist you in completing these
assignments.
At times, I will be using Mathematica during our classes to illustrate material we
are covering.
Tests: There
will be two self-scheduled mid-term exams and a final exam. Tentative dates:
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Search form
Math. for Elementary Teachers
Course Number:
MTH-217
Minimum Credits:
3
This course explores mathematics for elementary and middle grades teachers. Topics include sets, functions, logic, numeration, algorithms for basic computation, integers, rational numbers and their application, algebra concepts, probability and statistics. The course also introduces the NCTM standards and the Nebraska content standards for K-12 students. Upon successful completion, students will be able to present mathematics from a problem-solving perspective and integrate exploration and communication as methods of presenting mathematics to elementary and middle grades students. Prerequisite: Junior standing or permission. Offered fall term.
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Math Class Uses Free, Online Textbook
As a math professor, Joe Fields knows a thing or two about how costs can compound themselves. He can use algebraic
formulas – even calculus equations – to show just how much rising costs of higher
education are affecting the pocketbooks of students and their parents.
But he didn't need an advanced mathematical background to discover the effect that
rising textbook prices are having on students across the country, including those
he teaches at Southern.
That awareness helped spur Fields to write an open-source textbook for a course he
teaches on mathematical proofs. He makes the book available online for free to his
students, or for that matter to any students, professors or others who wish to read
it or print it out. "It just seemed ridiculous to me that a standard textbook for
this class was costing students around $150. So, I decided to write a book (A Gentle
Introduction to the Art of Mathematics) that is not only free, but that I believe
is better at helping students in their transition from computational math courses
to the more abstract and theoretical courses."
And don't worry, the quality is sound. In fact, his book has been endorsed by the
American Institute of Mathematics – a prestigious organization in the math world.
The book was originally published in 2008, but has had several revisions. A printed-on-demand,
hard copy of the book is also available for $14.40, but in the digital age, many students
are quite comfortable with reading online publications.
The approach taken by Fields – offering free online textbooks – is a growing phenomenon
in academia. At SCSU, several of his Math Department colleagues are following a similar path. Len Brin, assistant department chairman, has begun writing a book, "Numerical Analysis." And
Marie Nabbout-Cheiban, assistant professor, and Klay Kruczek, associate professor, are also involved in online software projects.
"You often see textbook publishers come out with revised editions after making only
minor changes that really didn't need to made," Fields said. "But they sometimes change
the numeric sequence of the math problems in the book so that students are forced
to buy the new edition, rather than purchase a cheaper, used book."
Fields said it is easier in some ways to develop and market such free online textbooks
for more advanced courses because there is less interest from publishing companies.
The introductory or more basic level courses are used by more students and the publishers
do a good job of providing supplemental materials, he said.
He typically teaches his Introduction to Proofs course to about 40 students a year.
That saves students – who in past years had been paying about $150 for a textbook
– a collective total of $6,000 a year. He does not know how many others have used
his textbook so far, but he has received a few emails – presumably from faculty members
or students at other schools -- asking questions about it.
Suzy Mitchell, an SCSU student who used the open-source book by Fields for another
math class, said she was pleasantly surprised by her experience. "I thought I was
going to hate an online textbook, especially a math one," Mitchell said. "However,
it was a very easy resource and as a student, it was very convenient and easy to access.
And the fact that the author of the book was one of my former professors was a great
comfort. If I was confused about something or questioned an idea, I could (ask) Dr.
Fields about it and he would be more than willing to help answer any of my questions."
Fields said he believes the use of open-source textbook will continue to grow.
"I think we are going to see increased interest and use of online books in higher
education as a way to help curtail costs for students," Fields said.
A recent report released by the U.S. Government Accountability Office shows an 82-
percent increase in the average price of college textbooks since 2002 -- virtually
triple the rate of inflation during that same period.
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Description of Saxon Calculus Homeschool Kit w/Solutions Manual by v
Based on Saxon's proven methods of incremental development and continual review strategies, the Saxon Calculus Homeschool Kit reviews key algebra, trigonometry and analytic geometry topics while introducing limits, functions, and the differentiation and integration of variables. This comprehensive text is ideal for future mathematicians, scientists and engineers!
Kit includes Student Textbook with 148 lessons, Homeschool Testing Book, Answer Key Booklet, and Solutions Manual with worked solutions to every problem in the textbook.
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08359119GF SUCCESS IN MATH: BASIC GEOMETRY SE 96
Success in Math helps students with varying learning styles master basic math concepts and prepares them for success on math competency tests.
Student Texts
This five-book softcover series breaks down core math concepts into short, manageable lessons that assume little background knowledge and are introduced in real-life context. In addition, chapter opener vocabulary lists and a glossary prove valuable for English language learners with below- or at-level math skills
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2Single Variable Essential Calculus
Summary
This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? SINGLE VARIABLE ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 550 pages--two-fifths the size of Stewart's other calculus texts (CALCULUS, Seventh Edition and CALCULUS: EARLY TRANSCENDENTALS, Seventh Edition) and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. SINGLE VARIABLE ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.
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Item Description: Wadsworth Publishing Company. Paperback. Book Condition: New. Paperback. 656 pages. Dimensions: 10.8in. x 8.4in. x 1.0in.Trust this market-leading text to give you a thorough introduction to mathematics methods and to provide you with a practical resource guide to teaching pre-school through sixth grade level mathematics. The texts This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9780495810971
Item Description: Cengage Learning. PAPERBACK. Book Condition: New. 0495810975 2010. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service!new_0495810975
Item Description: Cengage Learning 2010-06-15, 2010. PAPERBACK. Book Condition: New. 04958109750495810975ZN
Item Description: Cengage Learning. PAPERBACK. Book Condition: Good. 04958109750495810975
Item Description: Wadsworth Pub Co, 2010. Soft cover. Book Condition: New. BRAND NEW *** International Edition Softcover *** (No extra accessories). Printed in English with same contents to the US edition but different ISBN # and Cover Image. Some of them are printed on high quality color Glossy Paper. Some books may show sales disclaimer word such as "Not for Sale or Restricted in US" on the cover page but it is absolutely legal to use in USA or Canada. Delivery usually takes 3-5 Working days (Expedited Service) or 5-8 working days (Express) with tracking number provided. We do NOT ship to PO Box, FPO and APO addresses. Any question, please send to " ask seller a question " We will reply you ASAP. Thank you & enjoy buying. Bookseller Inventory # 030182
Item Description: Cengage Learning, 2010. Paperback. Book Condition: Used: Bookseller Inventory # 159495
Item Description: Cengage Learning, 2010. Book Condition: Used. This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed.usedgood_0495810975
Item Description: Wadsworth Publishing, 2010. Paperback. Book Condition: Acceptable. CONTAINS WATER DAMAGE / STAIN, STILL VERY READABLE, SAVE1039
Item Description: Wadsworth Publishing, 2010. Paperback. Book Condition: Good. Books have varying amounts of wear and highlighting. Usually ships within 24 hours in quality packaging. Satisfaction guaranteed. INSTRUCTORS EDITION ONLY28329150
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