清大數學系重量級教授退休前的最後一堂課，讓許世璧教授以嚴謹仔細的教學，讓你從源頭開始輕鬆理解ODE！沒上過許世璧教授的課，別說你懂常微分方程！體驗經典，就是現在！Want to understand ODE? Now, no longer hesitate, take the last chance to see how NTHU math titan, Prof. Sze-Bi Hsu copes well with this quite complicated subjects.
Course Description
本課程著重於常微分方程之定性理論,預備知識需高等微積分及線性代數.
本課程提供三學分的常微分方程基本理論，為研究生之標準課程。
This course focuses on the qualitative theory of ordinary differential equation, and preparatory knowledge of advanced calculus and Linear algebra. This course offers 3 credits of basic theory of ordinary differential equation, which is the standard course for graduates.
This course focuses on the qualitative theory of ordinary differential equation, and preparatory knowledge of advanced calculus and Linear algebra. This course offers 3 credits of basic theory of ordinary differential equation, which is the standard course for graduates.
指定用書
Textbooks
| ♠ | Sze-Bi Hsu: Ordinary Differential Equations with Applications. |
| World Scientific, 2013, 2nd edition |
參考書籍
References
References
| ♠ | Jack Hale: Ordinary Equations |
| ♠ | Jack Hale and Kocak: Dynamics and bifurcations |
教學方式
Teaching Method
Teaching Method
| ♠ | 演講及計算 |
| ♠ | Lecture and calculation |
教學進度
Syllabus
Syllabus
| 1. | Fundamental Theory of ODE: Existence: Uniqueness of System of ODE, Continuously |
| dependence on parameter and initial conditions, Differential Inequality | |
| 2. | Linear system : Linear systems with constant coefficients and Periodic Linear Systems, |
| Louiville Formula, Two-Dimensional Phase plane analysis, | |
| 3. | Stability of Nonlinear Systems: Linearization, Variation of Constant Formula,. Stable and |
| unstable manifolds, Orbital stability. |
