# Problem Sets

**Due Fri 12/3.**Problem Set 10.**Update 12/1:**Fixed a typo in Problem I.1. The denominator of E should be rho^3 not rho^3/2.**Due Fri 11/19.**Problem Set 9. Mostly stuff about Green's Theorem, plus a uniqueness theorem for solutions to Laplace's Equation (the kind of thing that (some) mathematicians find exciting!).**Update 11/17:**Fixed a typo in Problem I.3.b. The dot product of grad f with itself is the*square*of the length of grad f.**Due Fri 11/5.**Problem Set 8. This covers improper integrals, path/line integrals and surface integrals, which is quite a bit. Don't wait longer to start on it just because you have extra time. You'll want to study for the exam as well!Solutions to PS8. Full solutions this time.

**Due Fri 10/22.**Problem Set 7.Perhaps the best one yet.

**Due Fri 10/15.**Problem Set 6.**Update 10/14:**There was an error in the given formula for sin^4 t. All terms should be multiplied by an additional factor of 1/2. The posted version has the correction.Since Monday is a holiday, there will be no Monday office hours. I will have extra office hours both from 11-12 and 1-2 on Wednesday.

**Due Fri 10/8.**Problem Set 5. There is a Part I and a Part II, but they both fit on a single page. This shouldn't be as time consuming as psets 1, 2 and 3. (The algebra won't be as bad as pset 4 either; I actually checked this time.) This is about how long psets will be from now on.**Due Fri 10/1.**Problem Set 4. This is shorter, with no Part I problems, so you can focus on studying for Friday's midterm.**Due Fri 9/24.**Problem Set 3 (Part I), and (Part II).**Update 9/21:**Typo fixed on Part I, #2.a. The function should be e^{-1/t} for t > 0 and 0 for t <= 0. Typo fixed on Part I #3. The hint should index x by j, rather than i.**Due Fri 9/17.**Problem Set 2 (Part I), and (Part II).**Update 9/14:**Typo fixed on Part II, #2.b. The surface should be xyz = 1.**Update 9/13:**Clarification on #1, #2, and a typo fixed in #4 on Part I. (The hint is to use your result from #3, not #4).There are some proofs again, but I think you can do all of them without any epsilons or deltas.

**Due Fri 9/10.**Problem Set 1 (Part I), and (Part II).**Correction (9/8):**In I.4, the speed should be ||c'(t)||, not ||c(t)||. This has been corrected in the .pdf file.Part I contains the challenging theoretical problems for this week. Part II is more computational.

If you would like some practice with vectors, matrices and linear algebra, you can do the following optional problems (not to be handed in): Ch. 1.5: 1,3,5,7,13; Ch. 1 Review Exs: 11, 29. Solutions to these odd numbered problems are in the back of the book.

Since Monday is a holiday and I will not be on campus, I will have office hours both from 11-12 and 1-2 on Wednesday 9/8.