I have finished marking all of your submissions for Homework 8. Homework 9 is now available here. It will be due next Monday at 8.00 AM EDT (two hours later than usual because of the late posting).

I haven't made a final determination on office hour times yet. Tomorrow I will have the usual office hours from 1 -- 2 in Bahen 2139 and also an additional one from 12 -- 1 in the MAC in PG. I will let you know once I have decided what to do about Thursday.

Tomorrow I plan to work out an example using the eigenfunctions for the Laplacian on a cylinder which we found last Thursday and then (time permitting) introduce the eigenfunctions for the Laplacian on a sphere. It would be useful to review section 4.2.6 in the textbook for the latter topic. Going forwards, we will talk about solving the Poisson and heat equation with nonhomogeneous Dirichlet boundary conditions (and possibly Neumann or other boundary conditions as well, at least briefly); then we will take up the Fourier transform. I intend to talk about some integral representations of solutions to equations in connection with the Fourier transform, and then use the Fourier transform and our study of the eigenfunctions of the Laplacian to solve the wave equation in the three coordinate systems we have studied. Finally I intend to talk about some more theoretical aspects of the equations we have studied, and also (time permitting) some theoretical aspects of the separation of variables techniques we have been using. This will probably take us to the end of the term; if not I will talk briefly about asymptotic methods.

Let me know if you have any questions!

Nathan