10202常微分方程二Ordinary Differential Equations II

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