As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.
| Date | Class Topic | Reading (Nagle, Saff, Snider unless otherwise noted) |
|---|---|---|
| 1/16 | Course introduction; First order linear PDE | Lecture notes |
| 1/18 | More on 1st order linear PDE | Lecture notes |
| 1/23 | PDE models of transport, vibrations, diffusions | 10.1, 10.2 |
| 1/25 | The wave equation on R | Lecture notes |
| 1/30 | The heat kernel on R | Lecture notes |
| 2/1 | BVP's and Separation of Variables | 10.2 |
| 2/6 | More examples of BVP's | 10.2 |
| 2/8 | Fourier Series 1 -- orthogonality; Fourier coefficients | 10.3 |
| 2/13 | Fourier Series 2 -- examples | 10.3 |
| 2/15 | Fourier Series 3 -- pointwise convergence | 10.3 |
| 2/20 | Fourier Series 4 -- sine and cosine series | 10.4 |
| 2/22 | BVP's for the heat equation with one spatial dimension | 10.5 |
| 2/27 | BVP's for the wave equation with one spatial dimension | 10.6 |
| 3/1 | Spare day | |
| 3/6, 3/8 | No class -- Spring Break | |
| 3/13 | "Review" of Green's Theorem | Lecture notes |
| 3/15 | "Review" of surface integrals and Gauss's Theorem | Lecture notes |
| 3/20 | The wave and heat equations in 2 and 3 spatial dimensions | |
| 3/22 | BVP's for the heat equation on a rectangle | 10.5 |
| 3/27 | BVP's for the wave equation (rectangular drumhead) | 10.6 |
| 3/29 | Laplace's equation (equilibrium heat distribution) | 10.7 |
| 4/3 | Sturm-Liouville BVP's | 11.2 |
| 4/5 | Examples | 11.3 |
| 4/10 | The vibrating circular membrane | |
| 4/12 | No Class - Easter Recess | 8.6, 8.8 |
| 4/17 | Series solutions of Bessel's equation | 8.6 |
| 4/19 | More on Bessel Functions | 8.8 |
| 4/24 | The circular membrane -- examples | |
| 4/26 | Semester wrap-up |
Last modified: January 15, 2001