一、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。
二、指定用書(Text Books)
Sze-Bi Hsu: Ordinary Differential Equations with Applications. World Scientific, 2013, 2nd edition
三、參考書籍(References)
Jack Hale: Ordinary Equations
Jack Hale and Kocak: Dynamics and bifurcations
四、教學方式(Teaching Method)
演講及計算.
五、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.
4. Lyapunov functions.
六、成績考核(Evaluation)
Homework: 30%
Mid term :30%
Final Exam.: 40%
七、可連結之網頁位址