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- Academic unit or major
- Mathematics
- Instructor(s)
- Onodera Michiaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H137)
- Group
- -
- Course number
- ZUA.C331
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 1Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- 2019/5/7
- Language used
- English
- Access Index
-
Course description and aims
Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
Beginning with several fundamental results in (linear) functional analysis applied to linear partial differential equations, we learn fixed point theorems, topological degree and their applications to nonlinear partial differential equations.
This course is followed by Advanced courses in Analysis B.
Student learning outcomes
Understanding of the basic theory of nonlinear functional analysis including fixed point theorems and topological degree theory
Keywords
elliptic partial differential equations, functional analysis, fixed point theorems, topological degree
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Functional analysis and Sobolev spaces | Details will be provided during each class session. |
| Class 2 | Linear elliptic partial differential equations | Details will be provided during each class session. |
| Class 3 | Differentiable functionals | Details will be provided during each class session. |
| Class 4 | Fixed point theorem 1 | Details will be provided during each class session. |
| Class 5 | Fixed point theorem 2 | Details will be provided during each class session. |
| Class 6 | Topological degree theory 1 | Details will be provided during each class session. |
| Class 7 | Topological degree theory 2 | Details will be provided during each class session. |
| Class 8 | Other topics | Details will be provided during each class session. |
Textbook(s)
None
Reference books, course materials, etc.
- K. Masuda, Nonlinear mathematics (in Japanese), Asakura Shoten, 1985.
- L. Nirenberg, Topics in Nonlinear Functional Analysis (Courant Lecture Notes), AMS, 2001.
Assessment criteria and methods
Report (100%)
Related courses
- ZUA.C332 ： Advanced courses in Analysis B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to take Advanced courses in Analysis B (ZUA.C332).
Other
None
