Math 53 - Section 4 - Multivariable Calculus - Summer 2014
Preliminaries
Instructor: Kevin Wray
Lecture: MTWTF 2-3pm, Room: Evans 6
Discussion: MTWTF 3-4pm, Room: Evans 71
Office Hours: Tuesday and Thursday 1 - 2, Evans 741
Email: kwray[at symbol]math[dot]berkeley[dot]edu
Course Description
Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces.
Partial derivatives. Multiple integrals. Vector calculus.
Theorems of Green, Gauss, and Stokes.
Possibly (time permitting) an introduction to differential forms and de Rham cohomology.
Textbook
The textbook for this course is: Stewart, Multivariable Calculus: Early Transcendentals for UC Berkeley. (ISBN: 9781285132396, Cengage).
(This is a custom edition containing chapters 10 and 12-16 of Stewart's "Calculus: Early Transcendentals", 7th edition)
Grading and Course Policy (TENTATIVE)
There will be 5 take-home assignments. These assignments will count for 20% of your final grade. Students
are encouraged
to work together on these problems. However, each student must write their own solutions.
There will be 5 quizzes, the four highest scores will count for 15% of your final grade. There will be no
make-up quizzes.
There will be 2 midterms and a final. Your final grade will be computed as follows:
20% take-home sheets + 15% quizzes + 20% Max(midterm1,midterm2) + 20% Max(midterm2, final) + 25% final
Schedule
This is tentative!
Week 1
-
6/23 Vectors and dot products (12.1 - 12.3); Pactice Problems: 12.2 #21, #25 and 12.3 #28, #45
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6/24 Determinants and cross products (12.4); Practice Problems: 12.4 #7, #13, #19, #49, #53
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6/25 Matrices
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6/26 Equations of planes (12.5); Practice Problems: 12.5 #23, #25, #27, #31, #51
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6/27 Equations of lines (12.5); Practice Problems: 12.5 #5, #13, #45, #47
Week 2
-
6/30 Velocity and acceleration (13.1 - 13.4); Practice Problems: 13.1 #5, #7, #47, 13.2 #19, #25, 13.4 #11, #19
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7/1 Multivariable functions (14.1 - 14.3); Practice Problems: 14.1 #15 #27, 14.3 #33, #43, #53
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7/2 Approximation formula (14.4 and 14.7); Practice Problems: 14.4 #5, #13, #21, 14.7 #5, #13, #31, #35, #43
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7/3 Critical points (14.7); Practice Problems: 14.4 #5, #13, #21, 14.7 #5, #13, #31, #43
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7/4 No Class!
Week 3
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7/7 Differentials and the chain rule (14.4 and 14.5); Practice Problems:14.4 #33, #45; 14.5 #3, #5, #11, #47
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7/8 Gradient vectors (14.6); Practice Problems: 14.6 #7, #11, #19, #23, #29, #43(a), #67
-
7/9 Minimization - Lagrange Multipliers (14.7 and 14.8); Practice Problems: 14.8 #3, #11
#21, #27
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7/10 Non-independent variables (14.8) and Review for Midterm 1
-
7/11 Midterm 1
Week 4
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7/14 TBD
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7/15 Double Integrals (15.1 - 15.3); Practice Problems: 15.1 #17, 15.2 #9, #17, #35,
15.3 #21, #49
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7/16 Double integrals cont. (15.3 - 15.5); Practice Problems: 15.4 #11, #13, #15, #25
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7/17 Changing variables in double integrals (15.10); Practice Problems: 15.10 #4, #7, #17, #25, #27
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7/18 Vector fields and line integrals (16.1 and 16.2); Practice Problems: 16.2 #21, #39
Week 5
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7/21 Line integrals cont. (16.3); Practice Problems: 16.3 #25, #29, #35
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7/22 Gradient fields and potential functions (16.3 and 16.5); Practice Problems: 16.3 #7, #13, #15,
16.5 #15, #19
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7/23 Green's theorem (16.4 and 16.5); Practice Problems: 16.4, #7, #9, #17, #29
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7/24 Flux (16.5 and 16.7); Practice Problems: 16.5 #1, #7, #11, #21
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7/25 Green's theorem redux (16.4 and 16.5)
Week 6
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7/28 Triple integrals (15.7 and 15.8); Practice Problems: 15.7 #13, #19, #23, #35,
15.8 #17, #21
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7/29 Spherical coordinates (15.9); Practice Problems: 15.9 #17, #21, #29(a), #39
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7/30 Vector fields in space (16.1 and 16.7); Practice Problems: 16.7 #23, #27, #29
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7/31 Divergence theorem (16.5 and 16.9); Practice Problems: 16.9 #1, #7, #9
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8/1 Divergence theorem cont. (16.5 and 16.9); Practice Problems: 16.9 #25, #27, #29
Week 7
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8/4 Line integrals in space (16.2 and 16.3); Practice Problems: 16.2 #20, #21, #22
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8/5 Stokes theorem (16.8); Practice Problems: 16.8 #5, #7, #15, #17, #19
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8/6 Review for Midterm 2
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8/7 Midterm 2
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8/8 TBD
Week 8
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8/11 Midterm 2 solutions and tie up any loose ends
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8/12 TBD
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8/13 TBD
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8/14 Review for final
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8/15 Final
Homework
