Course Information
- Time: Mon 2-4 pm, Wed (biweekly) 10 am-12 pm
- Location: 三教 307
- Office hour: M622, Mon 4-6 pm or by appointment
- TA: 陈祚俣 (12432008 at sustech dot edu dot cn)
Lecture note and reference
references
- Tao Tang, Xuefeng Wang, Lecture notes on partial differential equations
- Evans, Lawrence C., Partial Differential Equations. Vol 19, Graduate Studies in Mathematics, AMS
- Strauss, Walter A., Partial Differential Equations: An Introduction. 2nd ed, Wiley, 2008
- 周蜀林, 偏微分方程, 北京大学出版社
- Courant, R., and Hilbert D., Methods of Mathematical Physics II: Partial Differential Equations. 1st ed, Wiley, 1989
- Qing Han, Fanghua Lin, Elliptic Partial Differential Equations. 2nd ed, AMS Lecture Notes.
Lecture note
| date | file |
|---|---|
| 9/11 | Lect 2 |
| 9/14 | Lect 3 |
| 9/23 | Lect 4 |
| 9/25 | Lect 5 |
| 9/30 | Lect 6 |
| 10/9 | Lect 7 |
| 10/14 | Lect 8 |
| 10/21 | Lect 9 |
| 10/23 | Lect 10 |
| 10/28 | Lect 11 |
| 11/11 | See the note above |
| 11/18 | See the note above |
| 11/20 | Lect 14 |
| Also see the note for some discussion on Fourier transforms | |
| 11/25, 27 | Lect 15 and 16 |
| 12/2, 4 | Lect 17 and 18 |
| 12/9 | Lect 19 |
| 12/16, 18 | Lect 20 and 21 |
| 12/23 | Lect 22 |
HW
- weekly; posted by Wednesday, due next Monday before class.
- Discussion and collaboration are encouraged, but names of the collaborators should be given in the submitted work.
| Assignments | Due date |
|---|---|
| HW1 | 9/23 |
| HW2 | 9/30 |
| HW3 | 10/14 |
| HW4 | 10/21 |
| HW5 | 10/28 |
| HW6 | 11/18 |
| HW7 | 11/25 |
| HW8 | 12/2 |
| HW9 | 12/9 |
| HW10 | 12/23 |
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. |