2021 Advanced topics in Analysis F1

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Onodera Michiaki 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue5-6()  
Group
-
Course number
MTH.C506
Credits
1
Academic year
2021
Offered quarter
4Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
English
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Course description and aims

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.

Student learning outcomes

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 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 - Topological degree theory 1 - Topological degree theory 2 - Implicit function theorem - Bifurcation theory 1 - Bifurcation theory 2 - Other topics 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

Report (100%)

Related courses

  • MTH.C351 : Functional Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None

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