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10201常微分方程一

2013-09-01-2014-01-01

國立清華大學 數學系 許世壁

關鍵字: 常微分方程一 Ordinary Differential Equations I I.V.P.解的唯一性 Uniqueness of solutions of I.V.P. 延續方案 Continuation of solutions 微分不等式 Differential Inequalities 指數矩陣 Exponential Matrix 丹表 Jordan Form

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.
 
 
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
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
 
Jack Hale: Ordinary Equations 
Jack Hale and Kocak: Dynamics and bifurcations 
 
 
教學方式
        
Teaching Method
 
 演講及計算
Lecture and calculation

 
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. 

 

前往課程 View Course
http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=98&
https://www.youtube.com/watch?v=DOOmy7x6gvE&list=PLS0SUwlYe8cwwCdIOiTo-8DYfMlhP2ooh