2021 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis E1
- 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.C505
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 3Q
- 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.
Beginning with several fundamental results in (linear) functional analysis applied to linear partial differential equations, we learn fixed point theorems and their applications to nonlinear partial differential equations.
This course is followed by Advanced topics in Analysis F1.
Course description and aims
Understanding of the basic theory of nonlinear functional analysis including fixed point theorems and their applications to nonlinear partial differential equations
Keywords
elliptic partial differential equations, functional analysis, fixed point theorems
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 | - Functional analysis and Sobolev spaces - Linear elliptic partial differential equations - Differentiable functionals - Fixed point theorems 1 - Fixed point theorems 2 - Other topics | 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
Report (100%)
Related courses
- MTH.C351 ： Functional Analysis
Prerequisites
None