2019 Advanced courses in Analysis A

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Academic unit or major
Mathematics
Instructor(s)
Onodera Michiaki 
Course component(s)
Lecture
Day/Period(Room No.)
Mon3-4(H137)  
Group
-
Course number
ZUA.C331
Credits
1
Academic year
2019
Offered quarter
1Q
Syllabus updated
2019/3/18
Lecture notes updated
2019/5/7
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.
Beginning with several fundamental results in (linear) functional analysis applied to linear partial differential equations, we learn fixed point theorems, topological degree and their applications to nonlinear partial differential equations.
This course is followed by Advanced courses in Analysis B.

Student learning outcomes

Understanding of the basic theory of nonlinear functional analysis including fixed point theorems and topological degree theory

Keywords

elliptic partial differential equations, functional analysis, fixed point theorems, topological degree

Competencies that will be developed

Intercultural skills Communication skills Specialist 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 Details will be provided during each class session.
Class 2 Linear elliptic partial differential equations Details will be provided during each class session.
Class 3 Differentiable functionals Details will be provided during each class session.
Class 4 Fixed point theorem 1 Details will be provided during each class session.
Class 5 Fixed point theorem 2 Details will be provided during each class session.
Class 6 Topological degree theory 1 Details will be provided during each class session.
Class 7 Topological degree theory 2 Details will be provided during each class session.
Class 8 Other topics Details will be provided during each class session.

Textbook(s)

None

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

  • ZUA.C332 : Advanced courses in Analysis B

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

Students are required to take Advanced courses in Analysis B (ZUA.C332).

Other

None

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