國立清華大學數學系
偏微分方程導論
Math 4280-00 (Spring 2024)  Introduction to Partial Differential Equations 

Textbook

Walter Strauss: Partial Differential Equations, An Introduction, Second Edition, 2008.

References

Lawrence C. Evans: Partial Differential Equations, Second Edition (Graduate Studies in Mathematics Vol 19) 2nd Edition, American Mathematical Society, 2010.

Course Description

This course is an introduction to the theory of partial differential equations intended for students majoring in mathematics. Our aim is to introduce basic concepts and techniques of partial differential equations. Throughout the course we will illustrate by some important mathematical models for problems from physics, such as wave propagation, diffusion, potential theory, heat transfer, etc. Students registering to this course should have some background knowledge on advanced calculus, linear algebra, and elementary differential equations. Topics to be covered include: 1. Where PDEs come from 2. Waves and Diffusions 3. Reflections and Sources 4. Boundary Problems 5. Fourier Series 6. Harmonic Functions 7. Green's identity and Green's Functions This course is an introduction to the theory of measure and integration.
In the second semester we will introduce some elements of functional analysis, abstract measure and integration. Topics to be covered include:  

1. Where PDEs come from

2. Waves and Diffusions

3. Reflections and Sources

4. Boundary Problems

5. Fourier Series

6. Harmonic Functions

7. Green's identity and Green's Functions

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 (M3M4R3R4), one is reserved for recitations (problem 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: Some problems from homework assignments will be collected and graded. Recitations (optional) are discussions of homework assignments. Click here for details. Further details will be available during the first week of classes.
Two exams (80%): Each exam worth 40% of the course grade. Dates of tests are on April 18 (Thursday) and June 17 (Monday).

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).