APM 346 Partial Differential Equations
- Some notes on the method of characteristics, using the radiative transport equation.
- Some problems and solutions for the first two weeks.
- Some more problems and solutions for the first two weeks.
- A primer on complex numbers and functions.
- Some problems for the first three weeks.
- A previous midterm to help prepare you for ours.
- Some problems for the first five weeks.
- Some problems on waves.
- Some problems on harmonic functions.
- Here are the scores on the first test.
- Here is a midterm to help prepare you for ours.
- Some problems on regular Sturm-Liouville ODE EVPs.
- Here is Kac's seminal paper. You can read pages 1-4. If you are inclined/interested you should also be able to read the whole thing.
- Here are the scores on the second test.
- Some problems on high-dimensional problems and Green's functions.
- Some problems on Fourier Transforms.
- A derivation of d'Alembert's formula via Fourier transform methods.
- Some selected solutions to the final problem set.
- A list of topics covered this term.
Some Solutions to Problems
- Here are some solutions, provided by students, to some of the Haberman problems.
- 1.2.6, 1.4.11 (continued), 1.5.3,
2.3.7, 2.4.4, 2.5.10, 2.5.13,2.5.14 (continued), 2.5.15,
3.2.2(continued) (continued) (continued) (continued), 3.3.6, 3.3.18, 3.6.2,
12.3.1 & 5, 12.3.4,
3.3, 188.8.131.52 (continued) (very nice), 5.5.7
- Online MAT346 book from previous year which we shall follow in part
- Guillaume Bal's course notes for a similar course at Columbia University in New York which we shall follow in part
- Wonderful Lecture notes from a similar course at MIT
- Mark Spiegelman's notes on conservation equations
- Gorgeous notes on the fundamental theorem of linear algebra (with pictures!) by Gilbert Strang