| Lec. | Date | Sec./pages covered | Topics |
|---|---|---|---|
| 1 | 8/23 | 17.2, 17.3: p. 850-851. |
Even, odd, and periodic functions - review. Fourier series of a periodic function. |
| 2 | 8/25 | 17.3 p.851-858 | Fourier series of a periodic function. |
| 3 | 8/30 | 17.5 | Manipulation of Fourier series. |
| 4 | 9/1 | 17.3 p.864-866 17.4 |
Complex exponential form for Fourier series. Half- and quarter-range expansions. |
| - | 9/6 | - Labor Day - | |
| 5 | 9/8 | Ch.9 17.6: p.881-882 |
Vector spaces -- review. Fourier series -- vector space approach. |
| 6 | 9/13 | 17.6: p.882-885 17.7 p.888-889 |
Fourier series -- vector space approach. Eigenvalues and eigenvectors -- review. Sturm-Liouville problem -- a simple example. |
| - | 9/15 | - classes cancelled - | |
| 7 | 9/20 | 17.7 p.887,891-893 | Sturm-Liouville problem -- setup and theorems. |
| 8 | 9/22 | 17.7 p.893-896 17.8 p.905-908 |
Sturm-Liouville problem -- examples. Periodic Sturm-Liouville problem. |
| 9 | 9/27 | Review | |
| 10 | 9/29 | Exam I | |
| 11 | 10/4 | 17.9 | Fourier integral. |
| 12 | 10/6 | 17.10 p.919-922 | Fourier transform -- definition and examples. |
| 13 | 10/11 | 17.10 p. 922-929 | Fourier transform -- properties and applications. |
| 14 | 10/13 | 18.2 p.944-948 |
More on Fourier transform. Partial differential equations. Classification of second order linear PDE. |
| 15 | 10/18 | 18.3 | Diffusion equation. |
| 16 | 10/20 | 18.3 | Diffusion equation -- separation of variables. |
| 17 | 10/25 | 18.3 p.965-968 | Diffusion equation -- use of Sturm-Liouville theory. |
| 18 | 10/27 | 18.3 p.968-971 | Unsteady conduction in a disk. |
| 19 | 11/1 | 18.4 p.981-986 | Heat conduction in an infinite rod. |
| 20 | 11/3 | Review | |
| 21 | 11/8 | Exam II | |
| 22 | 11/10 | 19.2 p.1023-25 |
Wave equation. Vibrating string -- separation of variables. |
| 23 | 11/15 | 19.2 p. 1026-28 19.4 p.1043-47 |
g(x)=0: modes; solution in a closed form. Vibrating string -- d'Alembert's solution. |
| 24 | 11/17 | 20.1 20.2 p.1059-63 |
Laplace equation. Separation of variables -- cartesian coordinates. |
| 25 | 11/22 | 20.3 p.1070-1072 |
Separation of variables -- cartesian coordinates. Separation of variables -- polar coordinates. |
| - | 11/24 | - Thanksgiving - | |
| 26 | 11/29 | 20.3 p.1073-75 | Dirichlet problem for circular disk. |
| 27 | 12/1 | 20.3 | Harmonic functions. |
| 28 | 12/6 | Review |