** Office hours:** M4-5, W3-4, F11-12

** Office:** APM 5256, tel. (858) 534-2734

** Teaching assistants:** Graham Hazel (ghazel@math.ucsd.edu) and
Daniel Felix (dfelix@math.ucsd.edu)

** Dates of exams: **

Midterms: 10/22 and 11/17 (new date !)

- H. Davis and A. Snider,
**Vector Analysis,**7/e wm. C. Brown Publishers 1995. - A. Shenk Handout available for download here: shenk.pdf

Marsden & Tromba,

and Barr

introduction. A brief text from a physics perspective is Shey

For lots of problems see Spiegel

For

differential equations Math 132A or physics classes in fluid mechanics and electromagnetism.

For the deeper analysis and proofs take Math 140, 142 or read e.g.:

Hubbard & Hubbard

Week 2: 2.1-2.2, 3.1-3.2 : Curves, velocity, tangents and arclength. Level surfaces and gradients.

Week 3: 3.3-3.5, 3.7 : Flow lines, divergence and curl. Taylors formula.

Week 4: 4.1-4.4,(4.5): Line integrals, simply connected domains, conservative and irrotational fields

Week 5: 15.1, 15.6 Double and triple integrals, change of variables, cylindrical and spherical coord.

Week 6: 4.6-4.8: Surface area, surface integrals and flux.

Week 7: 4.9: Introduction to Divergence Theorem and Stokes' Theorem.

Week 8: 4.9, 5.1 : Divergence Theorem.

Week 9: 5.4-5.5 , 5.2, (5.3): Greens and Stokes Theorems, Laplace Equation.

Week 10: (5.7)-5.8: Orthogonal transformations. Electromagnetism or Differential forms or Review.

Sections 15.1, 15.6 refers to the handout. Sections 1.1-1.13, 2.1-2.2 and 3.1-3.2 are review from 21C.

The change of variable theorem in the handout was not covered in 21C but is in the textbook for 21C.

** Homework assignments **

Homeworks need to be turned at ** the beginning **
of sections, and selected problems
will be graded. It is very important that you do the homework problems
as most of the exam problems
will be variations of homework problems.

for 10/2: Sec. 1.5: 3, 10, Sec. 1.7: 1, Sec. 1.8: 1, 8, Sec. 2.1: 1, Sec. 2.2: 2, 5, 8, Sec. 2.3: 3, 5,

for 10/9: Sec. 3.1: 1, 4, 5, 10b,c, 13, 32, Sec. 3.2: 2,4, Sec. 3.3: 3, 10, 11, Sec. 1.12: 1c, 3, 13, 22

for 10/16: Sec. 3.4: 3, 4, 6, 10, Sec. 3.5: 4, 9, Sec. 4.1: 1, 3, 4, 12,

for 10/23 (relevant for midterm!) Sec. 4.3: 1, 2ac, 3ac, 4, 5, 6, Sec. 4.4: 1ade, 6, 7, 10, Sec. 4.5: 2, 8, 9(no sketching required),

for 11/6: Sec. 4.6: 1, 3(don't worry about geometric interpretation), 5, 6, click on additional homework (updated on Monday 11/3) . Here are answers to some of the homework problems answers.

for 11/13: Sec. 4.7: 3, 4, 10, 11, 12, Sec. 4.8: 1, 4, 5, 6, Sec. 4.9: 3, 5, 21,

for 11/20: Sec. 5.4: 7, 8, 9, 12, Sec. 4.9: 11, 13, 15 16

for 12/4: (but get started, this will be a long assignment!) Sec. 4.9: 20, 21, 25, 26, Sec. 5.1: 6, 9, 10(you need not worry about expressing the vector field in terms of R and e_r), Sec. 5.5: 1,2, Sec. 5.2: 1, 5 (The earlier assigned problem 3 need not be turned in)

** Final:** Wednesday 12/10, 3-6pm

**Office hours for finals week:** Monday: 2-3, Tuesday: 1-2

**Info about final:** The usual rules apply:
You are allowed to use one hand-written cheat sheet,
but NO calculators, NO books, No other notes. Material goes over the
whole term. You can find practice finals with solutions on Lindblad's
webpage (click above at "additional info"). For our final, there might
be a little bit more emphasis on Stoke's theorem and the divergence theorem.
You could also practice doing surface integrals by looking at additional
problems in the book, such as Sect. 4.7: 5, 8, 9, Sect. 4.9: 7, 8, 10, 19.

** Second midterm: ** The second midterm takes place on Monday,
11/17 in the class room at the usual time. The rules are the same as
for the first one: You are allowed to use one hand-written cheat sheet,
but NO calculators, NO books, No other notes. The material goes over
the one covered in homework assignments from Sections 4.6-4.9
AND in the additional assignments posted as a pdf-file.
This does include e.g. the change of variable formula for double and triple
integrals, volume elements for spherical and cylindrical coordinates etc,
which are not contained in the Davis-Snider book!
It can be found in the Stewart calculus book, in the Shenk handout
(see URL listed above under `Texts') or, more concise, at
changevar; you need not know more than what we did in class.
Material from previous sections is only needed as far as it is
necessary for the current material.
You can find practice midterms with solutions on Lindblad's
webpage (click above at "additional info").
** Extra office hour:** Friday 11/14 after class.

** Midterm:** The first midterm takes place on Wednesday, 10/22
in the usual class room. You are allowed to use one hand-written cheat sheet,
but NO calculators, NO books, NO other notes besides the cheat sheet.
The problems will be similar to homework problems, with the material going
up to (including) Section 4.5. You can find practice midterms on
Lindblad's webpage which is mentioned above under additional information.
** Extra office hour:** Tuesday 1-2

for 10/7: p95: 1,2 (don't do part (b)), 5(a)-(d), 6, p.112: 4, 7, 9, 12, 14, 17

for 10/14: p.117: 1, 2 p.124: 1, 3, 7(NOT solution in book), 10, p.132: 1, 4, 9 (hint: use formula (3.41) on p.147 to show that a vector field can not be the curl of another vector field) p.135: 2, 3, 4,5

for 10/21: p.140: 5f-j, 7, 8, p.150: 3, 6, 8, 10g, p.169: 3, 4, 6 (only for cylindrical coordinates!) p.190: 1, 2, 3,

Practice problems for midterm: p.191: 12, 14, 19

for 10/28: p.204: 3a,d, 4, p. 212: 1b,d, 4, 7, 9, 10

for 11/4: p.236: 1, 3, 5, 6 (compute area whichever method you prefer; you can ignore (b) and (c)) p.246: 1, 3, 5, 8,

for 11/11: p. 256: 3, 4a-c, 6, p. 262: 1, 3, 5, 6

**Note:** Solutions for problems 1 and 3 on p. 236 are available
at Soft Reserve by 11/15.

for 11/18: p. 294: 6, 8, 9, 10, 12, p. 277: 7, 10

for 12/2: p. 262: 9a, 10, 15, 16, 26, 22, p. 299: 1,2,

additional exercises: p. 263: 17, 18, 25, p: 284: 1, 2 (ignore
the `solutions' at the end of the book for 2(a) and (b)),
** also** p. 212: 1a,c, 5,6,8

** Final **: Monday 12/13, 11:30 in class room. The usual rules apply:
1 cheat sheet allowed with hand-written information, no calculators, books
or other notes.

** Special office hours:** Arif Dowla: Sunday 12-3, 2325 APM,
Hans Wenzl, Sunday 3-4, 5256 APM.