偏微分方程(二)
Partial Differential Equations (II)
| 節 | 週四 | 週五 |
|---|---|---|
2 09:00–09:50 | 偏微分方程(二) SA214（光復） | |
3 10:10–11:00 | 偏微分方程(二) SA214（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
本課程屬大學部與研究所程度的微分方程課程,授課偏重於數學與物理間的連結,並且讓學生藉由此課程了解直觀地PDE概念。
Calculus, Linear algebra, Ordinary differential equation
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| 週次 | 主題 |
|---|---|
| 第 1 週 | waves in space: Ray, singularity, and sources, The diffusion and the Schrodinger equations |
| 第 2 週 | Boundaries in the plane and in space: Fourier's method, revisited. Vibration of a drumhead |
| 第 3 週 | Boundaries in the plane and in space: Solid vibrations in a ball, Nodes, Bessel functions |
| 第 4 週 | Boundaries in the plane and in space: Legendre functions, Angular momentum in quantum mechanics |
| 第 5 週 | General Eigenvalue Problems: The eigenvalues are minima of the potential energy, Computation of eigenvalues |
| 第 6 週 | General Eigenvalue Problems: Completeness, Symmetric differential operators |
| 第 7 週 | General Eigenvalue Problems: Completeness and separation of variables, Asymptotics of the eigenvalues |
| 第 8 週 | Distributions and Transforms: Distribution, Green's functions, revisited |
| 第 9 週 | Distributions and Transforms: Fourier transforms, Sources |
| 第 10 週 | Distributions and Transforms: Sources, Laplace transform techeniques |
| 第 11 週 | PDE problems from Physics: Electromagnetism, Fluids and accoustics |
| 第 12 週 | PDE problems from Physics: Scattering, Continuous spectrum |
| 第 13 週 | From now on, we use the second text book. Chapter 4. Other ways to represent solutions: 4.4 Converting nonlinear into linear PDE: Hoph-Cole transformation Potential functions |
| 第 14 週 | Chapter 4. Other ways to represent solutions: 4.4 Converting nonlinear into linear PDE: Homograph and Legendre transforms |
| 第 15 週 | 4.5 Asymptotics Singular perturbation |
| 第 16 週 | 4.5 Asymptotics Geometric optics, stationary phase |
| 第 17 週 | 4.5 Asymptotics Homogenization |
Partial differential equations, An Introduction Walter A. Strauss John Wiley & Sons, Inc. 2008 Partial Differential Equations Lawrence C. Evans AMS 1998
- 地點
- SA348
- 時間
- Thursday 4pm -5pm
- 聯絡方式
- Email: liming@math.nctu.edu.tw Tel: 56439