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!
【課程說明】 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。
【指定用書】
Textbooks
【參考書籍】
References
Jack Hale: Ordinary Equations
Jack Hale and Kocak: Dynamics and bifurcations
【教學方式】
Teaching Method
演講及計算.
【教學進度】
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. |