偏微分方程
Partial Differential Equations
| 節 | 週一 | 週五 |
|---|---|---|
3 10:10–11:00 | 偏微分方程 SA215 | |
5 13:20–14:10 | 偏微分方程 SA215 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
This course aims to teach some fundamentals of Partial differential equations (PDEs), a subject related to many branches of pure/applied mathematics and applied science. This one-semester course aims to introduce some analytical tools to analyze the existence, uniqueness, regularity of weak/classical solutions to first-order and second-order PDEs. In addition, students will learn to write clear, correct, rigorous proofs.
Calculus (along with multivariable calculus ), Advanced Calculus, Linear Algebra, ODE (not a prerequisite)
Homework 40% Report 30% Final Exam 30%
- Four important PDEs
- Non-linear first-order PDEs
- Some ways to represent solutions
- Function spaces
| 週次 | 主題 |
|---|---|
| 第 1 週 | Preliminary : Miltiindex, gradient, divergence, Gauss-Green Theorem, Green's formula, Polar coordinates formulas. |
| 第 1 週 | Ch 1 Introduction: linear/nonlinear, some examples, well-posed problems |
| 第 2 週 | The Mid-Autumn Festival |
| 第 2 週 | 2-1 Transport Equations |
| 第 3 週 | 2-2 Maximum Principle, Mollifier, Regularity, Harnack's Inequality |
| 第 3 週 | 2-2 Laplace Equation, Fundamental Solutions, Poisson Equation, Mean-Value Property |
| 第 4 週 | 2-2 Green's functions |
| 第 5 週 | 國慶連假 |
| 第 5 週 | 2-3 Fundamental solution for heat equations |
| 第 6 週 | 2-3 Initial value problems |
| 第 6 週 | 2-3 MVP for heat equation |
| 第 7 週 | Online 習題討論 |
| 第 7 週 | 2-3 Mean Value Principle for the heat equation |
| 第 8 週 | 2-3 Maximum Principle for the heat equation |
| 第 8 週 | 2-3 Maximum principle for the Cauchy problem |
| 第 9 週 | 2-4 Wave equation in 1D |
| 第 9 週 | 2-3 Regularity of solutions for the heat equation |
| 第 10 週 | Online 習題研討 |
| 第 10 週 | 2-4 Wave equation in 1D (cont.) |
| 第 11 週 | Midterm Presentation |
| 第 11 週 | Midterm Presentation |
| 第 12 週 | Midterm Presentation |
| 第 12 週 | 實體習題研討 |
Lawrence C. Evans. Partial Differential Equations. Second edition. Graduate Studies in Mathematics. David Gilbarg and Neil S. Trudinger, Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 edition. Springer, 2001. Walter A, Strauss. Partial Differential Equations: An Introduction. New York, NY: Wiley.
- 地點
- SA236
- 時間
- By appointment.
- 聯絡方式
- email: changhong@math.nctu.edu.tw