We will spend the first half of the course studying first-order equations. In particular, we will cover the method of characteristics for solving first-order equations and then move on to the discussion of weak solutions and conservation laws. The second half of the course will be devoted to the study of hyperbolic equations, with the main example being the wave equation. The material in this half of the course will include the method of separation of variables, Fourier series, Kirchoff's formula and Huygen's principle. At the end of this segment of the course, we will spend some time discussing hyperbolic systems.
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 one of the course assistants.
| Name | Class Time and Location | Office | Phone | Office Hours | |
|---|---|---|---|---|---|
| Julie Levandosky | TuTh 9:30-10:45; 380-380W | 382F | 723-4507 | Tu 1-3, Th 2-4 | julie@math.stanford.edu |
| Name | Office | Office Hours | |
|---|---|---|---|
| Yanping Pan | 380-380T | Tues. 2:30-5:30, Fri. 10-1 | yppan@math.stanford.edu |
| Kumar Muthuraman | 420-286 | Wed. 5:15-7:15 | mkumar@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 220A will be posted every week on Thursday. They will be due by 5:00 the following Friday.
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.
Both the midterm and the final will be in-class exams.
Midterm: Tuesday, Nov. 5, 2002: 9:30 a.m.-10:45 a.m.
Final: Thursday, Dec. 12, 2002: 12:15 p.m.-3:15 p.m., Location:
380-380W and 380-380Y