常微分方程(一)
Ordinary Differential Equations (I)
| 節 | 週三 | 週五 |
|---|---|---|
2 09:00–09:50 | 常微分方程(一) SA214 | |
3 10:10–11:00 | 常微分方程(一) SA214 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
This graduate-level course provides a rigorous introduction to the theory of ordinary differential equations (ODEs), where we will emphasize both analytical techniques and qualitative analysis. The course begins with foundational results on the existence and uniqueness of solutions for initial value problems, followed by a detailed study of linear systems, stability theory, and phase plane analysis. Students will also explore nonlinear systems, including the Hartman–Grobman theorem, and Lyapunov methods. Applications to physical, biological, and engineering systems will be discussed throughout the course to illustrate the theory.
微積分(Calculus)、線性代數(Linear Algebra)
Homework 70% Final Exam 30%
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction |
| 第 2 週 | 1.1 Existence and Uniqueness Theory, 1.2 Gronwall's Inequality and its applications, 1.3 Continuation of solutions |
| 第 3 週 | 1.4 Continuous Dependnece 1.5 Comparison Principle |
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Sze-Bi Hsu, Kuo-Chang Chen, Ordinary Differential Equations with Applications, 3/e Lawrence Perko, Differential Equations and Dynamical Systems Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2/e
- 地點
- SA236
- 時間
- 暫定周一 email約時間為主
- 聯絡方式
- changhong@math.nctu.edu.tw