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Lecture notes

0. Towards functional calculus
(lecture notes) (printable)
1. Hilbert spaces
(lecture notes) (printable)
2. Compact operators
(lecture notes) (printable)
3. A review of calculus
(lecture notes) (printable)
4. Fourier transform
(lecture notes) (printable)
5. Fundamental solutions
(lecture notes) (printable)
6. The Dirichlet problem
(lecture notes) (printable)
7. Measure theory
(lecture notes) (printable)
8. Integration theory
(lecture notes) (printable)
9. Function spaces
(lecture notes) (printable)
10. Radon-Nikodym derivatives
(lecture notes) (printable)
11. Spectral theory
(lecture notes) (printable)
12. Banach spaces
(lecture notes) (printable)

Problem sets

Assignments

Sample solutions are available on request.

Essay topics

A draft of your essay is due October 11 (end of week 10) and the final essay is due October 25 (end of week 11, the last week of classes). You're also welcome to come talk to me about your essay at any time, and ask for feedback on preliminary drafts. The essay is a substantial part of your assessment, and starting to think about it early will really pay off --- it should take some time to digest the material you're going to present, and work out the best way to explain it.

Final exam

You can see the questions that I decided not to use on the final exam. These are not representative of the actual questions!