傅立葉分析
Fourier Analysis and Applications
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 傅立葉分析 SA211（光復） | |
5 13:20–14:10 | 傅立葉分析 SA211（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
本課程介紹如何利用Fourier series 找出偏微分方程的解,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
無備註
版書
兩次期中考100%
Fourier series
Fourier sine series, Fourier cosine series,uniform convergence of Fourier series
Fourier method
Linear operator, principle of superposition, temperature problem, slab with internally heat
Fourier method
Vibration string problem, verification of solution
Boundary value problem
A string with initial velocity, an elastic bar, resonance, periodic boundary condition
Separation of variable
Heat equation
Separation of variable
Wave equation
Separation of variable
Laplace equation
Calculus of Fourier series
Differentiation of Fourier series, integration of Fourier series, Gibbs phenomenon
Sturm-Liouville eigenvalue problems
Introduction of Sturm-Liouville eigenvalue problems, Rayleigh quotient
Sturm-Liouville eigenvalue problems
Some PDE examples, homogeneous boundary conditions of the third kind
Classical PDE problems
Laplace equation in different coordinate systems
Classical PDE problems
Transverse vibrations of a thin beam
Classical PDE problems
Schrodinger equation
Fourier integral
Fourier sine integral, Fourier cosine integral
Fourier integral
Laplace transform and application
Fourier integral
Fourier transform solution method of PDEs
Fourier series
Inner product, orthonormal set, generlized Fourier series
| 週次 | 主題 |
|---|---|
| 第 1 週 | 2023-09-11(一),2023-09-13(三) |
| 第 2 週 | 2023-09-18(一),2023-09-20(三) |
| 第 3 週 | 2023-09-25(一),2023-09-27(三) |
| 第 4 週 | 2023-10-02(一),2023-10-04(三) |
| 第 5 週 | 2023-10-09(一),2023-10-11(三) |
| 第 6 週 | 2023-10-16(一),2023-10-18(三) |
| 第 7 週 | 2023-10-23(一),2023-10-25(三) |
| 第 8 週 | 2023-10-30(一),2023-11-01(三) |
| 第 9 週 | 2023-11-06(一),2023-11-08(三) |
| 第 10 週 | 2023-11-13(一),2023-11-15(三) |
| 第 11 週 | 2023-11-20(一),2023-11-22(三) |
| 第 12 週 | 2023-11-27(一),2023-11-29(三) |
| 第 13 週 | 2023-12-04(一),2023-12-06(三) |
| 第 14 週 | 2023-12-11(一),2023-12-13(三) |
| 第 15 週 | 2023-12-18(一),2023-12-20(三) |
| 第 16 週 | 2023-12-25(一),2023-12-27(三) |
Fourier Series and Boundary Value Problems, by James Ward Brown, Ruel V Churchill, 8th Edition, 2012
- 地點
- SA348
- 時間
- Thursday 4pm -5pm
- 聯絡方式
- Email: liming@math.nctu.edu.tw Tel: 56439