Advanced topics in Analysis F1

Academic unit or major

Graduate major in Mathematics

Instructor(s)

Michiaki Onodera

Class Format

Lecture

Media-enhanced courses

-

Day of week/Period
(Classrooms)

5-6 Tue

Class

-

Course Code

MTH.C506

Number of credits

100

Course offered

2021

Offered quarter

4Q

Syllabus updated

Jul 10, 2025

Language

English

Syllabus

Course overview and goals

Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
We study the topological degree, the implicit function theorem, and the bifurcation theory.
This course is following Advanced topics in Analysis E1.

Course description and aims

Understanding of the basic theory of nonlinear functional analysis including the topological degree, the implicit function theorem and the bifurcation theory

Keywords

elliptic partial differential equations, functional analysis, topological degree, implicit function theorem, 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

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

Report (100%)

Related courses

• MTH.C351 ： Functional Analysis

Prerequisites

None