You may bring in 2 normal 8.5x11 sheets of paper, with your own notes (written on both sides if you wish. So, you can use your 2 old ones, and add the new material on the backs)

Material will emphasize Boas chapters 2, 7, 15.4, 8, 12, and 13. (The parts we've covered) Look at your syllabus for more details - (Sections 4, 5 and 6). Approximately 25% of the exam will be older material that was covered in the first 2 exams. (See the previous two study sheets for help on that) Some places I noticed people needed some more work on were line integrals, scalar potentials, vector calculus in spherical and cylindrical coordinates... so there's a good chance you may see these!

As before, here are a few sample problems for the new material. 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. Don't forget to look over the previous exams, quizzes, and hw's, too!

Second half of section 4:

Applications: 2.5.68, 2.16.3, 2.16.6a, 2.16.8

Periodic Functions, SHM: 7.2.6, 7.2.8

Section 5:

Basics of Fourier series: 7.3.6

Average values: 7.4.14

Fourier sin-cos expansions: 7.5.2

Dirichlet conditions: 7.6.2

Fourier series in complex form: 7.7.2

Fourier series over other intervals: 7.8.2

Even and odd functions: 7.9.5, 7.9.16

Fourier transforms 15.4.4

Section 6:

1st order separable ODE's: 8.2.6, 8.2.22. (I might ask you to set up an ODE from a word problem, like any of 8.2.21- 8.2.30)

2nd order ODE's with constant coefficients: 8.5.5, 8.5.34 (sol'n to the latter is surely in your physics book from 1110), 8.6.5

Power series solutions: 12.1.7

Legendre functions: 12.2.1 (see eqn 12.2.7), 12.9.1

Orthogonal sets: 12.6.3, 12.7.1 (Boas doesn't have sol'ns to some of these last few problems, but they're essentially "show that"'s...)

Bessel functions: 12.15.7, 12.19.3

PDE's and boundary value probs: 13.2.12 (use Eq'n 13.2.17), 13.3.2, 13.4.6

Any additional material from lectures and homeworks remains fair game, as is material all the way up to the last day of class. 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.

Hope you enjoyed 2140, and got some useful tools out of it! See (some of) you in 2170! Happy holidays...