2026 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis A
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Michiaki Onodera
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Thu (M-107(H113))
- Class
- -
- Course Code
- MTH.C401
- Number of credits
- 100
- Course offered
- 2026
- Offered quarter
- 1Q
- Syllabus updated
- Mar 5, 2026
- Language
- English
Syllabus
Course overview and goals
This course covers the basic theory of second-order elliptic PDEs.
Using the Dirichlet problem as a central example, we introduce standard techniques including the maximum principle, Perron’s method, variational approaches, and the method of sub- and super-solutions.
We will also explore qualitative aspects of solutions, such as symmetry.
This course is designed to be followed by "Advanced Topics in Analysis B".
Course description and aims
Understanding of the basic theory of second order elliptic partial differential equations with emphasis on maximum principles
Keywords
elliptic partial differential equations, maximum principle, Perron’s method, sub- and super-solutions, method of moving planes
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course. Occasionally I will give problems for reports.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Harmonic functions |
Details will be provided during each class session. |
| Class 2 | Dirichlet problem |
|
| Class 3 | Perron’s method |
|
| Class 4 | Maximum principle |
|
| Class 5 | Method of sub- and super-solutions |
|
| Class 6 | Method of moving planes |
|
| Class 7 | Advanced topics |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2001.
Evaluation methods and criteria
Report (100%)
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C402 ： Advanced topics in Analysis B
- MTH.C351 ： Functional Analysis
Prerequisites
None
Other
None