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數學
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10202常微分方程二

2014-02-01-2014-06-01

國立清華大學 數學系 許世壁

關鍵字: 微分

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  
Ordinary differential equations has wide applications in all areas of natural science, social science, and is fundamental to other areas of mathematics, such as partial differential equations, geometry, and probability. This course is intended for graduate and advanced undergraduate students who have taken standard undergraduate courses for differential equations, linear algebra, and
complex analysis. Topics to be covered in the spring semester include Lyapunov stability, index theory, perturbation methods, Sturm-Liouville theoy, Hamiltonian systems.

Registered students are recommended to use the iLMS e-learning system
(http://www.nthu.edu.tw/elearning.php), where updates of the course will be posted. Contact your teaching
assistant if you have any question. 
 
 
指定用書
        Textbooks
Sze-Bi Hsu: Ordinary Differential Equations with Applications. 
 World Scientific, 2013, 2nd edition 
  
 
  
參考書籍
        References
 
E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations, 
 McGraw Hill, 1984.
R. Miller, A. N. Michel: Ordinary Differential Equations, Dover Publication, 1982.
  
  

  
教學方式
      Teaching Method
      演講及計算 Lecture and calculation
 
  
教學進度
      Syllabus
    ♠ Chapters 5-9 of the textbook. (tentative)
        Introduction
          Fundamental Theory
          Linear Systems
          Stability of Nonlinear Systems
          Method of Lyapunov Functions
          Two-Dimensional Systems
          Second Order Linear Equations
          The Index Theory and Brouwer Degree
          Perturbation Methods
          Introduction to Monotone Dynamical Systems

 

前往課程 View Course
http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=108&
https://www.youtube.com/watch?v=FML4m0Mf2Fo&list=PLS0SUwlYe8czP7IZa2rLwCylqlixPGgFe