I have posted lecture notes which I believe give fairly comprehensive coverage of this week's lectures here. I have also posted practice problems here. These are practice problems for just about everything we talked about this week, with an eye towards what might come up on the final more than towards what could reasonably be put onto the quiz. The quiz will be on things discussed on Tuesday or earlier. (In other words, don't stress about doing everything on the practice problems before Tuesday! There probably isn't time. The types of problems which might show up on the quiz are just those in practice problems 1 and 2 -- the rest involve stuff we didn't really cover until Thursday.)

Note that I do expect you to memorise the expressions for the eigenfunctions and eigenvalues. Thus for Tuesday's quiz you should memorise the expressions for the eigenfunctions and eigenvalues of the Laplacian on the cube Q and the cylinder C. (The eigenfunctions and eigenvalues on the ball B will not be on this week's quiz but you should memorise them for possible use on a future quiz, or on the final.)

Finally, there was an error on the homework assignment: in problem 2, the right-hand side should include a factor of r^2, not r^3. (Many thanks to the student who pointed this out to me!) I apologise for this and hope it did not cause too much trouble. I have posted an updated (and hopefully now correct!) version of the assignment on the course webpage here. (If you've already done it with r^3, instead of r^2, you don't need to re-do it to get full credit for this week's homework. However, since the type of problem that would show up on quizzes/the final would be of the form with r^2 instead of r^3, I highly recommend re-working it with the correct factor at some point -- though it needn't be right now.)

I think that's all for now -- best wishes with the homework! (And remember it isn't due until 8.00 AM, so you have an extra couple hours on Monday morning if you want.)

See you all Tuesday!

Nathan