Math 53 - Section 5 - Multivariable Calculus - Summer 2011
Preliminaries
Instructor: Kevin Wray
Lecture: MTWTF 12-1pm, Room: Evans 71
Discussion: MTWTF 1-2pm, Room: Evans 71
Office Hours: TBD, Evans 850
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: 978-1-4240-5499-2, Cengage).
(This is a custom edition containing chapters 10 and 12-16 of Stewart's "Calculus: Early Transcendentals", 6th edition).
Grading and Course Policy
There will be 5 take-home assignments. These assignments will count for 50% of your final grade. Students
are encouraged
to work together on these problems. However, each student must write their own solutions.
There will be 2 midterms. Only the higher of the two scores will count and this will make up 20% of your total grade. There will be
no make-up midterms.
There will be a final on the last day of class which will count for 30% of your grade.
Important Dates
This is tentative!
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6/23 HW 1 assigned - due 6/27
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6/30 HW 2 assigned - due 7/5
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7/8 Midterm 1
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7/14 HW 3 assigned - due 7/24
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7/21 HW 4 assigned - due 7/25
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7/28 HW 5 assigned - due 8/1
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8/4 Midterm 2
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8/12 Final
Resources
I have reserved a room, Cory 289, on Thursday afternoons 2-4. Use this room to work together on the take-home assignments, study for
upcomming exams or
just to hang out and get to know your colleagues.
Schedule
This is tentative!
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6/20 Vectors and dot products (12.1 - 12.3); Practice Problems: 12.2 #21, #25 and 12.3 #28, #43
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6/21 Determinants and cross products (12.4); Practice Problems: 12.4 #7, #13, #19, #45, #49
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6/22 Matrices
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6/23 Equations of planes (12.5); Practice Problems: 12.5 #23, #25, #27, #31, #49
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6/24 Equations of lines (12.5); Practice Problems: 12.5 #5, #13, #43, #45
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6/27 Velocity and acceleration (13.1 - 13.4); Practice Problems: 13.1 #5, #41, 13.2 #19, #25, 13.3 #25, #43, 13.4 #11, #19
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6/28 Multivariable functions (14.1 - 14.3); Practice Problems: 14.1 #7, #9, #13, #25, 14.3 #31, #41, #49
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6/29 Approximation formula (14.4 and 14.7); Practice Problems: 14.4 #5, #11, #21, 14,7 #7, #13, #31, #43
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6/30 Critical points (14.7); Practice Problems: 14.4 #5, #11, #21, 14,7 #7, #13, #31, #43
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7/1 Differentials and the chain rule (14.4 and 14.5); Practice Problems: 14.4 #33, #35, 14.5 #3, #5, #11, #47
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7/5 Gradient vectors (14.6); Practice Problems: 14.6 #7, #11, #19, #23, #29, #43, #63
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7/6 Minimization - Lagrange Multipliers (14.7 and 14.8); Practice Problems: 14.8 #3, #11
#19, #25, #45
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7/7 Non-independent variables (14.8)
and Review for midterm 1
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7/8 Midterm 1
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7/11 Day Off
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7/12 Double Integrals (15.1 - 15.3); Practice Problems: 15.1 #17, 15.2 #9, #17, #35,
15.3 #17, #45
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7/13 Double integrals cont. (15.3 - 15.5); Practice Problems: 15.4 #11, #13, #15, #25, 15.5 #5, #15
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7/14 Changing variables in double integrals (15.9); Practice Problems: 15.9 #7, #13, #21, #23
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7/15 Vector fields and line integrals (16.1 and 16.2); Practice Problems: 16.2 #3, #21, #33, #39
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7/18 Line integrals cont. (16.3); Practice Problems: 16.3 #7, #11, #23, #27, #33
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7/19 Gradient fields and potential functions (16.3 and 16.5); Practice Problems: 16.3 #13, #15,
16.5 #15, #19
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7/20 Green's theorem (16.4 and 16.5); Practice Problems: 16.4, #7, #9, #17, #27
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7/21 Flux (16.5 and 16.7); Practice Problems: 16.5 #1, #7, #11, #21, 16.7 #19, #21
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7/22 Green's theorem redux (16.4 and 16.5); Practice Problems: 16.5 #33, #35, #39
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7/25 Triple integrals (15.6 and 15.7); Practice Problems: 15.6 #11, #19, #23, #35, #39,
15.7 #17, #21
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7/26 Spherical coordinates (15.8); Practice Problems: 15.8 #17, #21, #29, #39
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7/27 Vector fields in space (16.1 and 16.7); Practice Problems: 16.7 #3, #15, #25, #37, #45
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7/28 Divergence theorem (16.5 and 16.9); Practice Problems: 16.9 #1, #7, #9, #19
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7/29 Divergence theorem cont. (16.5 and 16.9); Practice Problems: 16.9 #25, #27, #29, #31
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8/1 Line integrals in space (16.2 and 16.3); Practice Problems: 16.2 #11, #13, #35, #41, #43
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8/2 Stokes theorem (16.8); Practice Problems: 16.8 #5, #7, #15, #17, #19
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8/3 Review for Midterm 2
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8/4 Midterm 2
We are now going to jump into some advanced topics. In particular, we will go through the book
``Differential Forms: A Complement to Vector Calculus''
by Weintraub. However, none of this material will appear on the final.
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8/5 Differential forms and de Rham theory
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8/8 Manifolds
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8/9 Integration over manifolds
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8/10 The generalized Stokes' theorem
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8/11 Review for final
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8/12 Final
Take home assignments
Midterms
Final