2019 Advanced courses in Analysis B

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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.C332
Credits
1
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

Main subjects of this course are nonlinear functional analysis and its application to elliptic partial differential equations.
We study the implicit function theorem, bifurcation theory and variational methods.
This course is following Advanced courses in Analysis A.

Student learning outcomes

Understanding of the basic theory of nonlinear functional analysis including the implicit function theorem, bifurcation theory and variational methods

Keywords

elliptic partial differential equations, functional analysis, implicit function theorem, bifurcation theory, variational methods

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 Implicit function theorem Details will be provided during each class session.
Class 2 Bifurcation theory 1 Details will be provided during each class session.
Class 3 Bifurcation theory 2 Details will be provided during each class session.
Class 4 Deformation lemma Details will be provided during each class session.
Class 5 Mountain pass lemma Details will be provided during each class session.
Class 6 Symmetry and Compactness Details will be provided during each class session.
Class 7 Concentration-compactness principle 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.
- M. Willem, Minimax Theorems, Birkhauser, 1996.

Assessment criteria and methods

Report (100%)

Related courses

  • ZUA.C331 : Advanced courses in Analysis A

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

Students are required to complete Advanced courses in Analysis A (ZUA.C331).

Other

None

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