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- Academic unit or major
- Mathematics
- Instructor(s)
- Yanagida Eiji
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H137)
- Group
- -
- Course number
- ZUA.C334
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 4Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Reaction-diffusion equations are partial differential equations which mathematically describe the process of time evolution of spatial patterns, and are introduced as mathematical models for various phenomena in Biology, Physics, Chemistry, Population genetics and Neurophysiology. This course is intended to provide a fundamental mathematical theory for the equations. This course will follow "Advanced lectures in Analysis C".
Student learning outcomes
By the end of this course, students will be able to:
1) understand the properties of reaction-diffusion equations,
2) learn the method of analyzing the behavior of solutions.
Keywords
Reaction-diffusion equation, spatial pattern, stability
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 | Multi-component reaction-diffusion systems | Details will be provided during each class session. |
| Class 2 | Reduction of domains | Details will be provided during each class session. |
| Class 3 | Diffusion-induced instability | Details will be provided during each class session. |
| Class 4 | Gradient systems | Details will be provided during each class session. |
| Class 5 | Lotka-Volterra equations | Details will be provided during each class session. |
| Class 6 | FitzHugh-Nagumo equation | Details will be provided during each class session. |
| Class 7 | Ginzburg-Landau equation | Details will be provided during each class session. |
| Class 8 | Gierer-Meinhardt equation | Details will be provided during each class session. |
Textbook(s)
None
Reference books, course materials, etc.
Eiji Yanagida, Reaction-diffusion equations, University of Tokyo Press
Assessment criteria and methods
Reports (100%).
Related courses
- MTH.C341 ： Differential Equations I
- MTH.C342 ： Differential Equations II
- ZUA.C333 ： Advanced courses in Analysis C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students have passed ZUA.C333 ： Advanced courses in Analysis C
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
yanagida[at]math.titech.ac.jp
