(Issued Wed, Dec 6)

Due Wed, Dec. 13

Last homework, heck yeah!

Reminder: Final exam is Tues, Dec 19, 3:30-6:30

Required reading Boas 13.1-13.6

Note: This assignment will count just as much as any other homework, and this material will be on the final. In fact, you can expect something very similar to one (or at least part of one) of these problems to show up on the final...

(In all problems, please show your work clearly, especially since Boas gives the answer to most of these.)

1a) Boas 13.2.10. Note: .

b) 13.2.11 (See Boas' hint, no real algebra is required for this!)

2) 13.3.3 (Hints below, if you need them. Try it on your own first)

3a) What is the next term in the series in equation 13.4.9?

b) Boas 13.4.5

Hint: You may use the answer to Boas 7.9.23, which we already did in HW #12. [The answer to that one is also in the back of Boas, so you don't even need to dig out your old solutions] I claim that, armed with 7.9.23, both parts (a and b) of this problem can be done essentially by inspection, no real, algebra required.

Extra hint for 3b: Boas explains how it works in section 13.4 (around eqn 13.4.10 and 4.11.)

Hints for 2: This is a slightly tricky problem. It will help to first figure out the "steady state" solution as t goes to infinity. (See Boas' discussion around 13.3.7. Your function is very similar, but note that at large times, our problem goes to 100 at x=0, and 0 at x=l, i.e. slightly different than 13.3.7) You must simply add the steady state solution to your formal series, exactly like in Boas 13.3.16. Next, you need to figure out the "steady state" solution the slab is in just before t=0. (Here, 13.3.7 should be a big help!! Why?) In principle, your general solution can involve either sin(kx) or cos(kx) (like in Boas 13.3.10), but remember you are forcing u(0)=100 and u(l)=0 at ALL postive times! This makes you discard the cos terms (why?!) and forces k=n Pi/l (why?!) You will still have to do a Fourier sin series calculation, which involves one partial integration.