| Date | Topic | References |
| Friday, Sept. 11 | Intro, heat equation, | Chapters 1, 2, Wikipedia on Fourier |
| Monday, Sept. 14 | Derivation of Heat Eq., BCs | Chapters 3, 4, Vector space |
| Wednesday, Sept. 16 | Fourier series | Chapter 11, Wikipedia on Fourier |
| Friday, Sept 18 | Computation |
| Monday, Sept 21 | Complex basis, changes of variable, 2D | Wednesday, Sept. 23 | Fast Fourier Transform | Wikipedia on FFT |
| Friday, Sept 25 | Computation |
| Monday, Sept. 28 | Wave equation | Chapters 16, 19, 20 |
| Wednesday, Sept. 30 | Inner Product | ella notes on Inner Product |
| Friday, Oct 2 | Computation |
| Monday, Oct. 5 | Geometry of vector spaces | |
| Wednesday, Oct. 7 | Convergence issues | Uniform convergence |
| Friday, Oct 9 | Computation |
| Monday, Oct. 12 | BREAK | |
| Wednesday, Oct. 14 | Convergence Issues | |
| Friday, Oct 16 | Computation | Weierstrass M test |
| Monday, Oct. 19 | Self Adjoint operators | |
| Wednesday, Oct. 21 | Eigenvectors of Self Adjoint operators | |
| Friday, Oct. 23 | Variational characterization of eigenvectors |
| Monday, Oct. 26 | Spectral theorem | |
| Wednesday, Oct. 28 | Gaussian integration | |
| Friday, Oct. 30 | Computation |
| Monday, Nov. 2 | Circular drum | |
| Wednesday, Nov. 4 | Sturm-Liouville theory | |
| Friday, Nov 6 | Computation |
| Monday, Nov. 9 | Other drums I | Gordon/Webb article |
| Wednesday, Nov. 11 | Other drums II | Gordon/Webb article, Research Announcement |
| Friday, Nov. 13 | Computation |
| Monday, Nov. 16 | Non-linear problems, spectral methods | |
| Wednesday, Nov. 18 | Fermi Pasta Ulam problem | Friday, Nov 20 | Computation |
| Tuesday, Nov 23 | Plan projects? |
| Monday, Nov. 30 | Differentiability, Brownian motion | |
| Wednesday, Dec. 2 | Autocorrelation | |
| Friday, Dec 4 | Computation |