Some comments about Homework 5. There were multiple papers which tried to solve problem 1 by splitting the interval into pieces based on the definition of the piecewise function and then finding series expansions of the initial data on each subinterval separately; this often led to the assumption that only l = 0 or at most l = -1, 0, 1 needed to be considered. I apologise for being so direct but I really need to emphasise that this method of approaching the problem is simply completely wrong and would result in little or no credit on the term test. (As I have mentioned before, `completed' on the homework merely means that you have made some effort towards solving the problem -- a solution marked `completed' on the homework might in fact be given 1/10 or less if given on a test.) This is closely related to the fact that the coefficients in an expansion in orthogonal functions cannot depend on the spatial variables (e.g., x and y when we were dealing with Laplace's equation on a square, or theta and phi more recently).

If you feel that you are having trouble with this, please write me or come talk to me either around class or in office hours and I will do my best to explain things.

I received an inquiry as to whether I will be posting solutions to the suggested practice problems from the textbook. I do not intend to do so -- there are answers in the textbook (p. 514); if you have specific questions feel free to ask me about them in office hours or at some other point.

As mentioned previously, readings for today include the readings suggested last week (3.2, especially 3.2.1, 3.2.3, 3.2.5, and 3.2.7); also 3.5.2 is useful.

As you can see from Homework 6, I have become pessismistic about our ability to cover the heat equation before the term test (i.e., by this Thursday). In the event that we do have time to say something about the heat equation I intend to add an extra assignment (with probably just one question) to be due sometime before the term test, on the heat equation.

Finally, due to personal commitments elsewhere I will probably have to leave immediately after class today so I unfortunately won't have time to stick around to answer questions.

See you all this afternoon!

Nathan