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.
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
References
| ♠ | |
| McGraw Hill, 1984. | |
| ♠ | |
教學方式
Teaching Method
♠演講及計算 Lecture and calculation
教學進度
Syllabus
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
