MAT
230 – Multivariable Calculus
Syllabus
Class Time:
Text: Calculus,
7th edition , Larson, Hostetler, Edwards.
Instructor:
André Wehner, Olin 111, Ph.
238-5919, e-mail wehner@centre.edu,
Office Hours:
Study Sessions:
Grading: 3 tests @ 15% each = 45%
Final 25%
10 quizzes @ 3% each = 30%
Course Description
This course
is meant to familiarize you with the exciting world of geometry and
differentiable functions in dimensions higher than two.
We will
work our way through chapters 10-14 of the text. Calculus I and II (chapters
1-9 of our text) are prerequisites for this class. There is a website
accompanying our text at http://college.hmco.com/mathematics/larson/calculus_analytic/7e/students/index.html
. They have rotatable graphs, chapter summaries, practice tests and other
useful stuff. More calculus resources on-line can be found under http://archives.math.utk.edu/calculus/crol.html#software
.
Before we
dive into the calculus of several variables, we will study what is known as the
Analytic Geometry of two-space and three-space. We will describe vectors,
lines, planes, and surfaces in space analytically. We will use Cartesian
coordinates and two non-Cartesian coordinate systems, spherical and
cylindrical. Naturally this involves a good deal of spatial sense. Maple comes in very handy here. I will
pass out worksheets
on the relevant Maple commands in
class.
With this
background, we can then do calculus in higher dimensions by first extending the
definitions of limit, derivative and integral to vector-valued functions and
functions of several variables. We will study partial differentiation and its
application to finding extrema. We will calculate double, triple, line, and
surface integrals, and learn some of the important theorems from vector
calculus.
Further
Remarks
You are
expected to be present for all classes. Please let me know in advance if you
must be absent for a scheduled college activity. Three inexcused absences will
result in a lowering of the grade.
Homework is
an essential part of this class, even though they are not to be turned in. I
only assigned odd-numbered problems, so you know the answers from the back of
the book. You are expected to spend about 4 to 5 hours per week on homework.
You are encouraged to work together and make use of Maple 7 for visualization
and to check your answers. Maple is available in the labs listed here.
The quizzes
(10 minutes), tests (1 hour), and the final (2 hours) will consist of a
selection of the assigned homework problems. They are “closed everything.” You
may use single-line scientific calculators, but not graphing calculators. You
must show all work.
The quizzes
will be given at the beginning of class. If you are late, you will not be given
extra time. If you have to miss class for a valid reason (proof required!), you
will be allowed to make up a quiz or test. If you know in advance you will miss
a test or quiz, you should make arrangements to take it early.
If you do the
homework, you should do fine in this class. Expect to be graded on a 90-80-70
scale, depending on the class average.
In
cooperation with the disability resource center, reasonable accomodation will
be provided for students with disabilities. Please meet the instructor during
the first week of class to make suitable arrangements.
This
syllabus is available online at http://web.centre.edu/wehner/courses/m230f02.htm
.
Schedule
|
Day |
Material Covered |
Homework |
|
|
|
|
|
9/2 |
Introduction; 10.1 |
10.1: 9, 27, 37, 41, 47, 51, 55, 63, 71, 73, 81, 85, 91, 95 |
|
9/4 |
10.2 |
10.2: 7, 27, 29, 31, 35, 37, 39, 41, 47, 51, 55,
57, 63, 67, 71, 75, 89, 97, 99, |
|
9/6 |
Quiz 1; 10.3; 10.4 |
10.3: 5, 7, 9, 17, 19, 27, 31, 37, 39, 43, 47, 63, 67, 71, 75, 77 10.4: 9, 15, 29, 31, 35, 37, 43, 47, 57, 59, 61, 63 |
|
9/9 |
10.5 |
10.5: 5, 7, 9, 13, 15, 17, 19, 25, 29, 31, 35, 37, 41, 43, 45, 51, 59, 63, 67, 69, 71, 75, 77, 81, 87 |
|
9/11 |
10.6 |
10.6: 1-6, 9, 11, 17, 19, 23, 25, 27, 29, 31, 33,
35, 37, 39, 41, 43, |
|
9/13 |
Quiz 2; 10.7 |
10.7: 5, 11, 13, 15, 17, 19, 21, 23, 29, 35, 39, 41, 43, 47, 81-86, 91, 93, 95, 97, 99, 101, 103, 105, 107 |
|
9/16 |
11.1 |
11.1: 3, 7, 13, 15, 17-20, 21, 23, 27, 31, 33, 37, 45, 47, 49, 51, 55, 57, 59, 61, 69, 71, 75, 77, 85, 89 |
|
9/18 |
11.2 |
11.2: 1, 3, 7, 11, 15, 19, 23, 37, 39, 41, 45, 47, 53, 55, 59, 67, 71, 73 |
|
9/20 |
Quiz 3; 11.3 |
11.3: 1, 5, 9, 15, 21, 25, 29, 37, 41, 43, 45, 47, 51 |
|
9/23 |
11.4 |
11.4: 1, 5, 9, 15, 19, 27, 37, 47, 49, 57, 63 |
|
9/25 |
11.5 |
11.5: 1, 3, 5, 7, 15, 17, 19, 21, 27, 31, 33, 35, 37, 39, 51, 53, 55, 63, 67, 69, 71, 75, 79, 81, 85, 87, 89, 91 |
|
9/27 |
Test 1 (Ch.10-11) |
|
|
9/30 |
12.1 |
12.1: 1, 3, 5, 11, 13, 17, 19, 23, 29, 31, 33, 35, 37, 45-48, 51, 53, 55, 69, 71, 73, 83, 85, 87, 89 |
|
10/2 |
12.2 |
12.2: 1, 7, 9, 11, 17, 19, 25, 33, 35, 37, 41, 45, 55, 57 |
|
10/4 |
Quiz 4; 12.3 |
12.3: 1, 3, 5, 13, 17, 25, 29, 33, 35, 37, 45, 47, 49, 53, 55, 57, 71, 75, 77, 91, 93, 97, 99, 101 |
|
10/7 |
12.4 |
12.4: 1, 3, 13, 15, 17, 25, 31, 33, 35, 37, 39, 41, 45 |
|
10/9 |
12.5 |
12.5: 1, 3, 5, 9, 11, 13, 15, 19, 21, 23, 27, 29, 31, 33, 39, 43, 51, 55, 57, 59, 61, 63 |
|
10/11 |
Quiz 5; 12.6 |
12.6: 1, 5, 11, 13, 17, 21, 23, 27, 29, 31, 33, 39, 41, 43, 45, 55, 57, 63, 73, 77, 79, 81 |
|
10/14 |
12.7 |
12.7: 1, 3, 5, 7, 11, 15, 17, 19, 25, 29, 33, 39, 43, 47, 49, 51, 53, 55 |
|
10/16 |
12.8 |
12.8: 1, 3, 7, 13, 21, 23, 27, 31, 33, 43, 45, 47, 51, 53, 63 |
|
10/21 |
Quiz 6; 12.9 |
12.9: 1, 3, 5, 7, 9, 13, 15, 19, 21 |
|
10/23 |
12.10 |
12.10: 1, 3, 5, 9, 11, 13, 15, 19, 23, 25, 27, 31, 37 |
|
10/25 |
Test 2 ( |
|
|
10/28 |
13.1 |
13.1: 3, 5, 9, 13, 15, 21, 23, 29, 31, 33, 35, 37, 39, 41, 47, 51, 53, 57, 59, 61, 63, 65, 69, 77 |
|
10/30 |
13.2 |
13.2: 1, 7, 9, 11, 13, 15, 17, 21, 25, 27, 33, 35, 39, 49, 51, 53, 55, 67, 73, 75, 77 |
|
11/1 |
Quiz 7; 13.3; 13.4 |
13.3: 9, 11, 15, 17, 21, 23, 27, 29, 31, 33, 35, 55, 57 13.4: 1, 3, 5, 7, 11, 13, 15, 27, 29, 31 |
|
11/4 |
13.5 |
13.5: 1, 3, 5, 11, 13, 15, 19, 21, 29, 31, 33, 33, 37, 39 |
|
11/6 |
13.6 |
13.6: 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, 31, 33, 35, 37, 47, 51, 53 |
|
11/8 |
Quiz 8; 13.7 |
13.7: 1, 3, 5, 9, 11, 13, 15, 17, 21, 23, 27, 29, 33, 35, 37, 45 |
|
11/11 |
13.8 |
13.8: 1, 3, 5, 7, 9, 11, 15, 17, 19, 27, 29 |
|
11/13 |
14.1 |
14.1: 1-6, 7, 9, 11, 13, 17, 19, 21, 25, 27, 29, 31, 33, 35, 43, 45, 47, 51, 53, 57, 59, 61, 69, 71, 73, 75, 77-84, 85 |
|
11/15 |
Quiz 9; 14.2 |
14.2: 1, 3, 5, 7, 9, 11, 13, 19, 21, 23, 29, 31, 35, 37, 39, 43, 49, 51, 53, 55, 57, 63 |
|
11/18 |
14.3 |
14.3: 1, 3, 5, 11, 15, 17, 19, 21, 25, 27, 35, 37, 47, 49, 51 |
|
11/20 |
14.4 |
14.4: 1, 3, 7, 9, 11, 17, 19, 21, 23, 25, 27, 41, 47, 49 |
|
11/22 |
Test 3 (13.1-14.4) |
|
|
11/25 |
14.5 |
14.5: 1-4, 5, 7, 9, 13, 19, 21, 23, 25, 31, 33, 35, 37, 39, 49, 51 |
|
12/2 |
14.6 |
14.6: 1, 3, 5, 13, 15, 17, 19, 23, 25, 27, 29, 37 |
|
12/4 |
Quiz 10; 14.7 |
14.7: 1, 3, 5, 7, 9, 11, 17, 21, 25, 27 |
|
12/6 |
14.8 |
14.8: 3, 7, 9, 11, 21, 25 |
|
|
|
|
|
12/11 |
Final (comprehensive) |
|