Math
283 Honors Multivariate Calculus (Fall 2010)
| Instructor |
Mark
Pernarowski |
| Textbook |
Multivariate
Calculus (6th ed.) |
|
James Stewart |
| Office
Hours |
Schedule
(Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil
1-144 |
|
 |
Grading: The course % is determined by:
Midterm 1 M1 100
Midterm 2 M2 100
Final F 100
Quizzes Q 100
_________________________________
400
% = (M1+M2+F+HW)/4
The final is not comprehensive.
Six quizzes each worth 20 points
will be given. Your best 5 quiz
scores determine Q above.
Exam and quizz dates are indicated
on the schedule below. Their content
will be announced in class.
All exams and quizzes are closed
book and no electronic devices
are permitted. All exams will be
given in class.
|
Syllabus: Material covered in text is from:
Chapter 12 Vector Geometry
Chapter 13 Vector Functions
Chapter 14 Parital Derivatives
Chapter 15 Multiple Integrals
Chapter 16 Vector Calculus
Homework: Suggested homework is listed below.
Although the homework is not graded
it is representative of the kinds of
questions which will be on quizzes
and exams.
Some additional problem sets and/or
handouts will be handed out in class
and/or posted on this site.
|
Exam
and Quiz Schedule: All
exams and quizzes are closed book. No
electronic devices are permitted.
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Aug
30 |
31 |
Sept
1 |
2 |
3 |
| |
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|
| 6 |
7 |
8 |
9 |
10 |
| Labor
Day |
|
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|
Quiz 1
|
| 13 |
14 |
15 |
16 |
17 |
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|
|
|
20 |
21 |
22 |
23 |
24 |
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|
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Quiz 2 |
| 27 |
28 |
29 |
30 |
Oct
1 |
| |
|
|
|
Midterm 1 |
| 4 |
5 |
6 |
7 |
8 |
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| 11 |
12 |
13 |
14 |
15 |
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Quiz 3 |
| 18 |
19 |
20 |
21 |
22 |
| |
|
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|
|
| 25 |
26 |
27 |
28 |
29 |
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Quiz
4 |
| Nov
1 |
2 |
3 |
4 |
5 |
|
Election Day
|
|
|
Midterm
2 |
| 8 |
9 |
10 |
11 |
12 |
| |
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Veterans Day |
|
| 15 |
16 |
17 |
18 |
19 |
| |
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|
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Quiz 5 |
| 22 |
23 |
24 |
25 |
26 |
| |
|
Thanksgiving |
Thanksgiving |
Thanksgiving |
| 29 |
30 |
Dec
1 |
2 |
3 |
| |
|
|
|
Quiz 6 |
| 6 |
7 |
8 |
9 |
10 |
| |
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| 13 |
14 |
15 |
16 |
17 |
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Final |
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FINAL
EXAM: Thursday, Dec 16, 8:00-9:50am (Wilson 1-144)
Suggested
Homework: (Subject to revision
as course develops)
| 12.1 |
7,11,13,15,20 |
Cartesian
coordinates, distance, spheres |
| 12.2 |
13,17,19,21,41 |
Vectors,
vector addition and length |
| 12.3 |
5,7,9,17,21,23,25,27,35,37 |
Dot
product and geometric properties |
| 12.4 |
1,3,15,19,27,31,43 |
Cross
product and geometric properties |
| 12.5 |
7,10,11,15,19,23,27,33,35,43,53,55,62,69 |
Equations
of lines and planes |
| 12.6
|
none |
Quadratic
surfaces |
| 13.1 |
1,7,9,25,27,37h |
Vector
functions, curves |
| 13.2 |
3,5,9,11,13,19,21,23,31,33,34 |
Vector
function calculus, tangent vectors |
| 13.3 |
1-3,11,13,17,19,21,25,43 |
Arclength,
curvature, normal and binormals |
| 13.4 |
3,5,9,15,22,33,35 |
Velocity,
acceleration |
|
Midterm
1 : Friday Oct 1 |
On
all material above excluding curvature. |
|
|
Review
problems Chapters
12-13 |
| 14.1 |
11,13,39,41,47 |
Functions
of several variables, domain, range |
| 14.2 |
7,9,11,15,25,29,33,39 |
Limits
and continuity |
| 14.3 |
5,15,17,19,21,25,39,45,47,51,61 |
Partial
derivatives, tangents to surfaces |
| 14.4 |
1,3,11,13,21 |
Tangent
planes and linear approximations |
| 14.5 |
1,5,7,9,13,15,21,27,31,49 |
Chain
rules, implicit differentiation |
| 14.6 |
4,5,7,9,11,21,25,39,41,47,61 |
Gradients,
directional derivatives, level sets, geometry |
| 14.7 |
1,5,7,9,11,15,29,31,39,43 |
Maxima,
minima, second derivative test |
| 14.8 |
3,5,7,9,25,27,31,33,39 |
Lagrange
multipliers, constrained maximization |
|
Midterm
2: Friday
November 5 |
All
material on
Chapter 14 excluding max on regions |
|
|
Some
problems
Chapter
14 |
| 15.1 |
none |
Double
integral definition |
| 15.2 |
1,3,5,7,9,15,25,29 |
Double
iterated integrals |
| 15.3 |
1,3,7,13,15,19,21,23,25,39,41,43,45,51 |
Double
integrals on regions, reversing integration order |
| 15.4 |
5,7,9,11,13,19,20,25,29,31 |
Double
integrals in polar coordinates |
| 15.5 |
none |
Applications
of double integrals |
| 15.6 |
3,9,11,13,17,19,21,31 |
Triple
cartesian integrals, volumes |
| 15.7 |
1,3,7,9,11,15,17,19,21,23a,27 |
Triple
integrals in cylindrical coordinates |
| 15.8 |
1,3,7,9,11,13,21,23,25,27,39 |
Triple
integrals in spherical coordinates |
| 15.9 |
1,3,11,13 |
Double
integrals in arbitrary coordinates |
| 16.1 |
11-14 |
Vector
fields, gradient fields |
| 16.2 |
1,5,7,9,13,15,19,22,41 |
Scalar
and vector line integrals |
| 16.3 |
3,5,9,12,13,14,15,19,21 |
Potentials,
path independence and the Fundamental Thm. |
| 16.4 |
1,5,11,13,17 |
Greens
Theorem in the plane,
|
| 16.5 |
1,3,5,13,17,31,35 |
Curl
and
Divergence of a Vector Field |
| 16.6 |
1,5,19,23h,37,38,39,41,43,47,59 |
Areas
for graphs and parametric
surfaces |
| 16.7 |
5,7,11,15,19,22,23,29 |
Surface
integrals and Flux |
| 16.8 |
2,3,7,9,11a |
Stokes'
Theorem |
| 16.9 |
1,3,5,11,13 |
Divergence
Theorem |
|
Final:
Thursday Dec 16,
8-9:50am in Wil 1-144 |
Material
in
Chapters 15,16 above |
|
|
problems here.
Formula sheet here.
|
|
|
Some old
exams (less useful, without solutions) here |
Handouts:
- Review
questions and solutions for Chapters
12-13
- Review
questions and solutions for Chapter 14
- Summary
of integration formulae
- Review
questions for Chapter 15-16
Examples
of exams and quizzes for the
non-honors Multivariate Calculus course (M224) I have taught in past
years can be found here.
You will note both *.pdf and *.tex files. Mathematicians often use a
typsetting program called latex
to create the nicely typeset formulae in texts and papers. If you are
interested you can look at the *.tex files used to create those exams
(what I have to edit to make your tests for instance).
Other
Stuff:
The
scientific process
Here are some links to a few cool sites related to the content of this
course:
Graphing
Tools
Barbara Koskosz (University of Rhode
Island)
Simple
Calculus
WebMathematics Interactive
Multivariate
Demos
Jonathon Rogness University of Minnesota
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