一、課程說明(Course Description)
<br>
<br>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.
<br>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。
<br>
<br>
<br>
<br> 二、指定用書(Text Books)
<br>
<br>Sze-Bi Hsu: Ordinary Differential Equations with Applications. World Scientific, 2013, 2nd edition
<br>
<br> 三、參考書籍(References)
<br>
<br>Jack Hale: Ordinary Equations
<br>Jack Hale and Kocak: Dynamics and bifurcations
<br>
<br>
<br>
<br>
<br>
<br>
<br> 四、教學方式(Teaching Method)
<br>
<br>演講及計算.
<br>
<br>
<br>
<br> 五、教學進度(Syllabus)
<br>
<br>1. Fundamental Theory of ODE: Existence: Uniqueness of System of ODE, Continuously 
<br>dependence on parameter and initial conditions, Differential Inequality.
<br>2. Linear system : Linear systems with constant coefficients and Periodic Linear Systems, Louiville 
<br>Formula, Two-Dimensional Phase plane analysis,
<br>3. Stability of Nonlinear Systems: Linearization, Variation of Constant Formula,. Stable and unstable 
<br>manifolds, Orbital stability.
<br>4. Lyapunov functions.
<br>
<br>
<br>
<br> 六、成績考核(Evaluation)
<br>Homework: 30%
<br>Mid term :30%
<br>Final Exam.: 40%
<br>
<br>
<br>
<br>
<br> 七、可連結之網頁位址
<br>
<br>  
<br>
<br>
<br>