2018 Advanced topics in Analysis C

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Yanagida Eiji 
Course component(s)
Lecture
Day/Period(Room No.)
Fri3-4(H137)  
Group
-
Course number
MTH.C403
Credits
1
Academic year
2018
Offered quarter
3Q
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 be followed by "Advanced topics in Analysis D".

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

Intercultural skills Communication skills Specialist 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 Reaction-diffusion models Details will be provided during each class session.
Class 2 Various types of special solutions Details will be provided during each class session.
Class 3 Properties of scalar reaction-diffusion equations Details will be provided during each class session.
Class 4 Scalar reaction-diffusion equation on a bounded domain Details will be provided during each class session.
Class 5 Scalar reaction-diffusion equation on a bounded interval Details will be provided during each class session.
Class 6 Fujita equation Details will be provided during each class session.
Class 7 Fisher equation Details will be provided during each class session.
Class 8 Nagumo 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

Repots (100%).

Related courses

  • MTH.C341 : Differential Equations I
  • MTH.C342 : Differential Equations II
  • MTH.C404 : Advanced topics in Analysis D

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

Students are expected to have passed MTH.C341: Differential Equations I and MTH.C342: Differential Equations II.

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