國立清華大學數學系

常微分方程一

Math 5250-00 (Fall 2025) Ordinary Differential Equations I 

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 is a year-long course 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 fall semester include:

1. Fundamental theory

2. Linear systems 

3. Local stability of nonlinear systems

4. Method of Lyapunov functions

Syllabus: 

Click HERE for details.

Textbook: 

Sze-Bi Hsu, Kuo-Chang Chen: Ordinary Differential Equations with Applications, 3rd edition, World Scientific, 2022. 

References:

[1] Vladimir I. Arnold: Ordinary Differential Equations, Universitext, Springer, 1992.

[2] E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations, McGraw Hill, 1984.