2021 Advanced topics in Analysis E1

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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.C505
Credits
1
Academic year
2021
Offered quarter
3Q
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.
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

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