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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yanagida Eiji
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- MTH.C402
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 2Q
- Syllabus updated
- 2016/4/27
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course follows Advanced topics in Analysis A.
This course begins with nonlinear differential equations and continuous dynamical systems, local properties, especially the notion of stability. Also, this course discusses the existence of various orbits and their geometric properties.
Student learning outcomes
Students will understand fundamental notions and methods of nonlinear analysis, and apply them to some examples.
Keywords
Nonlinear differential equation, continuous dynamical system, stability, orbit
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 differential equation | Details will be provided during each class session. |
| Class 2 | Theory of continuous dynamical systems | Details will be provided during each class session. |
| Class 3 | Stability | Details will be provided during each class session. |
| Class 4 | Stable manifold and unstable manifold | Details will be provided during each class session. |
| Class 5 | Homoclinic orbit | Details will be provided during each class session. |
| Class 6 | Periodic orbit | Details will be provided during each class session. |
| Class 7 | Homotopy method | Details will be provided during each class session. |
| Class 8 | Bifurcation theory | 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
- MTH.C401 ： Advanced topics in Analysis A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to have completed Advanced topics in Analysis A (MTH.C401).
Other
None in particular
