國立清華大學數學系
微分方程
Math 3010-00 (Fall 2026)  Differential Equations  

Course Description

This course is an introduction to the theory of differential equations intended for second or third year undergraduate students majoring in mathematics. Our aim is to introduce basic concepts, techniques, and applications of first and second order linear equations. Some methods for nonlinear equations and higher order systems will be briefly outlined. Topics to be covered include:

1. First order differential equations

2. Second order linear differential equations

3. Higher order linear differential equations

4. Series solutions

5. Laplace transforms

6. Nonlinear equations and stability

7. Boundary value problem

Textbook

W. Boyce, R. DiPrima, D. Meade: Elementary Differential Equations and Boundary Value Problems, 12th ed., John Wiley & Sons, 2022

References

M. Hirsch, S. Smale, R. Devaney: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Elsevier Academic Press, 2004.
S.B. Hsu, K.C. Chen: Ordinary Differential Equations With Applications, 3rd ed., World Scientific, 2022.

Syllabus

Click HERE for details. Note that this is a 3-credit course, so in average there will be 3 hours of classes every week. Among the 4 scheduled class hours (M1M2R1R2), one is reserved for recitation (discussion) sessions, instructed by teaching assistants.

Attendance

Students are expected to attend every scheduled class. It is the student's responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.
 

Grading

Homework/Quizzes: Selected exercises from the textbook will be assigned. Click HERE for details. Quizzes will be taken place during recitations, and will be based on homework assignments. Further details will be available during the first week of classes.
Two exams: Dates of tests are on October 29 (Thursday), and December 21 (Monday).

There are two ways to count your course grades, whichever is in your favor:
(1) Quizzes 30%, Midterm 35%, Final exam 35%.
(2) Midterm, Final exam, each worth 1/2 of course grade.

Absence from exams

You should miss an exam only for the most compelling reasons and you should obtain permission in advance (except in some extraordinary circumstances). If you miss an exam for legitimate reasons, then a make-up exam will be arranged.