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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kagei Yoshiyuki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(M-110(H112))
- Group
- -
- Course number
- MTH.C506
- Credits
- 1
- Academic year
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- 2023/3/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
This course is concerned with fundamental methods in the mathematical analysis of nonlinear partial differential equations. More concretely, I will explain introductory topics from fixed point theorems, degree theory, variational method and bifurcation theory.
This course is following Advanced topics in Analysis E1.
Student learning outcomes
Understanding of fundamental methods in nonlinear functional analysis and their applications to nonlinear partial differential equations
Keywords
Nonlinear analysis, fixed point theorems, degree theory, variational method method and bifurcation theory
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 | 1. Preliminaries 2. Fixed point theorems 3. Degree theory 4. Variational method 5. Bifurcation theory | Details will be provided during each class. |
Out-of-Class Study Time (Preparation and Review)
Enough preparation and review if necessary
Textbook(s)
Not required
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
Attendance and report
Related courses
- MTH.C351 ： Functional Analysis
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to have taken the course "Advanced topics in Analysis E1".
