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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.C505
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 3Q
- 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.
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.
Student learning outcomes
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 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 | - 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. |
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
