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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Onodera Michiaki
- Class Format
- Lecture
- Media-enhanced courses
- 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
- Access Index
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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
