2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis F1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yoshiyuki Kagei
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue (M-110(H112))
- Class
- -
- Course Code
- MTH.C506
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
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
- 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 | 1. Preliminaries 2. Fixed point theorems 3. Degree theory 4. Variational method 5. Bifurcation theory | Details will be provided during each class. |
Study advice (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.
Evaluation methods and criteria
Attendance and report
Related courses
- MTH.C351 ： Functional Analysis
Prerequisites
Students are required to have taken the course "Advanced topics in Analysis E1".