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- Academic unit or major
- Mathematics
- Instructor(s)
- Yanagida Eiji
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- ZUA.C331
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 1Q
- Syllabus updated
- 2016/4/27
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course begins with the notion of differentiation of nonlinear operators, and discusses the existence of fixed points and its application, and the reduction to finite dimensions.
Student learning outcomes
Students are expected to understand fundamental notions and methods of nonlinear analysis, and apply them to some examples. This course is followed by Advanced courses in Analysis B.
Keywords
Nonlinear operator, nonlinear analysis, reduction
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Nonlinear operator | Details will be provided during each class session. |
| Class 2 | Gateaux derivative, Frechet derivative | Details will be provided during each class session. |
| Class 3 | Contraction mapping principle | Details will be provided during each class session. |
| Class 4 | Banach's perturbation theorem | Details will be provided during each class session. |
| Class 5 | Newton's method | Details will be provided during each class session. |
| Class 6 | Implicit function theorem | Details will be provided during each class session. |
| Class 7 | Nonlinear compact operator | Details will be provided during each class session. |
| Class 8 | Lyapunov-Schmidt reduction | Details will be provided during each class session. |
Textbook(s)
None in particular
Reference books, course materials, etc.
None in particular
Assessment criteria and methods
Based on overall evaluation of the results for report and final examinations. Details will be announced during a lecture.
Related courses
- ZUA.C332 ： Advanced courses in Analysis B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis B (ZUA.C332).
Other
None in particular
