| 週次 |
授課內容 |
| 第1週 |
Chapter 1. Where PDEs Come From
1.1 What is a Partial Differential Equation?
1.2 First-Order Linear Equation |
| 第2週 |
1.3 Flow, Vibrations, and Diffusions
1.6 Types of Second-Order Equations |
| 第3週 |
Chapter 2. Waves and Diffusions
2.1 The Wave Equation |
| 第4週 |
2.2 Causality and Energy
2.3 The Diffusion Equation |
| 第5週 |
2.4 Diffusion on the Whole Line |
| 第6週 |
Chapter 3. Reflections and Sources
3.1 Diffusion on the Half-Line
3.2 Reflections of Waves |
| 第7週 |
3.3 Diffusion with a Source |
| 第8週 |
3.4 Waves with a Source
3.5 Diffusion Revisited |
| 第9週 |
Midterm I |
| 第10週 |
Chapter 4. Boundary Problems
4.1 Separation of Variables, The Dirichlet Condition
4.2 The Neumann Condition |
| 第11週 |
4.3 The Robin Condition
Chapter 5. Fourier Series
5.1 The Coefficients |
| 第12週 |
5.2 Even, Odd, Periodic, and Complex Functions
5.3 Orthogonality and General Fourier Series |
| 第13週 |
5.4 Completeness
Chapter 6. Harmonic Functions
6.1 Laplace’s Equation |
| 第14週 |
6.2 Rectangles and Cubes |
| 第15週 |
6.3 Poisson’s formula
6.4 Circles, Wedges, and Annuli |
| 第16週 |
Final Exam |
| 第17週 |
自主學習 |
| 第18週 |
自主學習 |