偏微分方程導論
Introduction to Partial Differential Equations
| 節 | 週二 | 週四 |
|---|---|---|
5 13:20–14:10 | 偏微分方程導論 SA311（光復） 2 節連堂 | |
6 14:20–15:10 | ||
7 15:30–16:20 | 偏微分方程導論 SA311（光復） |
* 根據陽明交大上課時間表所列
Partial differential equations are an important mathematical tool for solving problems in science and engineering. This course hopes to guide students in learning the theory and application of partial differential equations. Course Overview: This course will introduce in detail various basic partial differential equations, from first order to second order, from linear to nonlinear, from basic theory to practical application; it will also allow students to understand the application of these partial differential equations in physics, engineering and other scientific fields. Main Objectives: 1. Understand the basic concepts and classification of partial differential equations. 2. Master the skills of solving first-order and second-order partial differential equations, including separation of variables method, eigenvalue method and transformation method. 3. Learn to apply partial differential equations to solve practical problems such as heat conduction, waves, and electromagnetism.
1. Calculus (including vector calculus) 2. Linear algebra
無備註
以版書講授為主。
Midterm exam 35%,Final exam 35%,Classwork and quizzes 30%。
Introduction to PDE
1. First and second order PDE 2. Classification of PDE 3. Well-posedness of PDE
- 講授：
- 2 weeks
Evolution equations on the line
1. Wave and diffusion equations in dimension 1+1 2. Boundary value problems 3. Separation of variables
- 講授：
- 3 weeks
The Fourier series
1. definitions, convergence, applications, etc.
- 講授：
- 3 weeks
Harmonic functions
1. The Laplace equation 2. Poisson formula, maximum principle, etc. 3. Examples for domains with symmetry
- 講授：
- 3 weeks
Green’s functions
1. Green’s identities 2. Green’s functions 3. Applications
- 講授：
- 2 weeks
Wave equations in space
1. The wave equation in dimension 1+3 2. Boundary value problems in space
- 講授：
- 2 weeks
Other topics
(Schrodinger’s equation, eigenvalue problems, etc.; if time permits)
| 週次 | 主題 |
|---|---|
| 第 1 週 | 2025-02-18(二),2025-02-20(四) |
| 第 2 週 | 2025-02-25(二),2025-02-27(四) |
| 第 3 週 | 2025-03-04(二),2025-03-06(四) |
| 第 4 週 | 2025-03-11(二),2025-03-13(四) |
| 第 5 週 | 2025-03-18(二),2025-03-20(四) |
| 第 6 週 | 2025-03-25(二),2025-03-27(四) |
| 第 7 週 | 2025-04-01(二),2025-04-03(四) |
| 第 8 週 | 2025-04-08(二),2025-04-10(四) |
| 第 9 週 | 2025-04-15(二),2025-04-17(四) |
| 第 10 週 | 2025-04-22(二),2025-04-24(四) |
| 第 11 週 | 2025-04-29(二),2025-05-01(四) |
| 第 12 週 | 2025-05-06(二),2025-05-08(四) |
| 第 13 週 | 2025-05-13(二),2025-05-15(四) |
| 第 14 週 | 2025-05-20(二),2025-05-22(四) |
| 第 15 週 | 2025-05-27(二),2025-05-29(四) |
| 第 16 週 | 2025-06-03(二),2025-06-05(四) |
Partial Differential Equations, Second Edition, Walter A. Strauss.
- 地點
- 科學一館338室
- 時間
- By appointment
- 聯絡方式
- carstea@nycu.edu.tw