In this course, we will cover techniques involved in solving parabolic and elliptic partial differential equations. In particular, we will study the heat equation, the Laplace equation, Fourier series, eigenvalue problems, Green's functions, properties of harmonic functions, potential theory, the Fourier transform and calculus of variations.
No knowledge of partial differential equations is assumed. However, a solid foundation in multivariable calculus is required. Some knowledge of ordinary differential equations will be useful. If you have not taken an ODE course, however, you should still be able to pick up the necessary background in that area.
While no knowledge of PDE is required, the course will move at a good pace. If you have any questions regarding course material, you should feel free to come see me or the course assistant.
| Name | Class Time and Location | Office | Phone | Office Hours | |
|---|---|---|---|---|---|
| Julie Levandosky | MTuWTh 2:15-3:05; 380-380W | 382F | 723-4507 | MTuW 3:15-4:30 p.m., Tu 12:00-1:00 p.m. | julie@math.stanford.edu |
| Name | Office | Office Hours | |
|---|---|---|---|
| Dimitrios Cheliotis | 380M | W 12:00-1:00 p.m. | dimitris@math.stanford.edu |
The following textbooks are recommended: Partial Differential Equations: An Introduction by Walter Strauss and Partial Differential Equations by Lawrence Evans. I will not be following either of them section by section, but most of the material I cover will be included in one of these texts. Strauss' book is an upper-level undergraduate text. Evans' book is a graduate text and requires a solid mathematical background. Some students may find it difficult to read at first. However, by reading slowly and carefully, you will grow to appreciate it.
Both textbooks will be on reserve in the Mathematics library on the fourth floor of building 380.
The course grade will be based on the following.
Homework: 20%
Midterm: 30%
Final Exam: 50%
Homework assignments for Math 220B will be posted every week by Thursday. In general, they will be due in class the following Thursday. (Except the week of the midterm, in which case the homework will be due on Tuesday.)
You are permitted to collaborate on the homework; however, you must write up your homework yourself. You should not copy somebody else's homework: if you choose to collaborate, you should be able to recreate all of the steps involved in solving a problem yourself, and should do so in your writeup.