- Time: Tue 10 am - 12 pm, Thur 10 am - 12 pm (biweekly)
- Location: 三教 304
- Office hour: Wed 10 am - 12 pm, M622
- TA: 程子苓 (chengzl@sustech.edu.cn)
Lecture note and reference#
lecture note (last update: Oct 10)
- Evans, Lawrence C., Partial Differential Equations. Vol 19, Graduate Studies in Mathematics, AMS
- 周蜀林, 偏微分方程, 北京大学出版社
- Qing Han, Fanghua Lin, Elliptic Partial Differential Equations. 2nd ed, AMS Lecture Notes.
- Strauss, Walter A., Partial Differential Equations: An Introduction. 2nd ed, Wiley, 2008
- Courant, R., and Hilbert D., Methods of Mathematical Physics II: Partial Differential Equations. 1st ed, Wiley, 1989
weekly; posted by Thursday, due next Tuesday before class.
Grading scheme#
| % | |
|---|
| Participation | 5% | |
| HW assignments | 20% | weekly |
| Mid-term | 25% | |
| Final | 50% | |
Schedule (tentative)#
| Lecture | Content |
|---|
| 1 | Introduction to PDEs: important examples, classical solutions, initial values and boundary conditions, well-posedness, classification. |
| 2 | First-order equations: transport problem, methods of characteristics, formation of shocks. |
| 3-6 | Parabolic (Heat) equation: Fourier transform, fundamental solutions; maximum principle and energy estimates; mixed boundary conditions |
| 7-11 | Elliptic equations: Laplace and Poisson’s equation; harmonic function, mean-value properties, maximum principle; fundamental solutions, Green’s functions; energy method; eigenvalue problem and separation of variables, Parron’s method. |
| 12 | Midterm |
| 13-16 | Wave equation: solutions formula in dimension 1, 2 and 3; domain of influences; separation of variables, plane and traveling waves. |
| 17-20 | Calculus of Variation: Sobolev spaces, weak solutions and convergence, Lax-Milgram Theorem |
| 21-23 | Nonlinear first-order equations: Hamilton–Jacobi equation, entropy solutions, shocks, Hopf–Lax formula. |