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