After much labor and revising (though certainly nowhere near close to sufficient, particularly as concerns the latter), the lecture notes for this week (with a brief mention of one of the first results we will derive next week) are available here. They are rather long and contain rather more information than we have discussed yet in lecture. While I think all of the information in them is useful (well, almost all; perhaps not the jokes), at a first go one should focus only on the first one or two examples of sequences having the properties of the delta function in the limit (pp. 4--8), and those of you who have not studied epsilon-delta proofs can skip them. I do hope though that the last example (on pp. 7--8) may clarify the expression for the delta function in spherical coordinates which we gave in class. The introductory paragraph about Fourier transforms, where I introduce without careful explanation eigenfunctions with periodic boundary conditions, can be read fast; the point is the series expansion, not that the individual functions are eigenfunctions of the Laplacian, nor the boundary conditions they satisfy (though these are interesting problems). Of the properties of the Fourier transform mentioned, the first two are the most important, though (c) is helpful for Homework 10, and (d) and (e) are good to know. Finally, as usual, information in the footnotes is of a more supplementary character.

So, to sum up: one can skip a few of the examples on pp. 4--8 and most of what is in the footnotes, but pretty much everything else is important to know about.

I have also posted some practice problems here. Many of these require somewhat more theoretical thinking than the problems in this course have heretofore been wont to require.

Homework 10 remains unchanged (it can be solved using some of the results in the lecture notes which were not covered in lecture).

As far as what next week's quiz will cover: basically everything from eigenfunctions of the Laplacian on the unit ball through the introduction to Green's functions which we had on Tuesday, and material related to the first problem on Homework 10. Fourier transforms and the more detailed study of Green's functions we did on Thursday will not be on the quiz.

Let me know if you have any questions!

Nathan