Once again, you may bring in a normal 8.5 x11 sheet of paper, with your own notes written on one  side only. Please hand your note sheet in along with the exam. (I'll return it to you.)

Material will be primarily from Boas chapters 5, 6 and the beginning of 2. Look at your syllabus for more details. (Exam 2 will cover syllabus sections 2 and 3, and the start of 4)

As before, here are a few sample Boas problems. These are NOT required by any means - but if you feel shaky on a topic, use the problems to help you clarify what you don't understand. Schey's "Div, grad, curl and all that" - available as a reference book in the physics and engineering libraries (and in the bookstore), Ch.'s II and III provides a nice alternative perspective, and many good (worked and homework) examples!

1. Surface integration, how to find mass, centroid, moment of inertia (also in polar coordinates, and also over curved surfaces) (5.2.25, 5.3.7, 5.4.1b,c, 5.5.1, 5.5.5, [I get 32[[pi]] for the last]). 5.5.9

2. Volume integrals, Fluxes, divergence theorem, , Gauss's law.

5.4.5, 6.10.2, 6.10.4, 6.10.8 (answer: 80[[pi]], can you do it both ways?), 6.10.14, 6.11.6

3. Stokes Theorem, , and conservative fields. Boas 6.11.4, 6.11.7, 6.11.12, 6.12.25. Also, if you need to review line integrals: Boas 6.8.1, 6.8.7b,d

4. Laplacian, , and other expressions involving . (including other coordinate systems) Boas 6.7.10, 6.7.16, 6.7.19, 10.9.16 Can you show that the identity (i) in the table at the end of Ch. 6 follows from the triple cross product rule for vectors?

5. Complex numbers: (rect. and polar form, products and quotients, conjugates, etc. Boas: 2.5.6, 2.5.19, 2.5.25, 2.5.30, 2.5.55 (a: horizontal), 2.9.34

6. Powers, roots, and other fns of complex numbers. Boas 2.10.7, 2.10.21, 2.11.9, 2.14.2

Any additional material from lectures and homeworks is also fair game. I consider those things which I spent time deriving/proving to be important, and you might be expected to be able to sketch those derivations/proofs.