Course title
V04407002
Mathematics for Phenomena

 ISHIWATA Tetsuya Click to show questionnaire result at 2019
Course description
In this lecture, you study mathematical analysis of mathematical models in physics, chemistry, biology and so on. The main topics are the followings: The stability theory
of dynamical systems, the behavior of solutions to the Hamilton system, gradient systems and so on.
Purpose of class
To understand the phenomena in several sciences, you understand the mathematical modelling and mathematical analysis for mathematical models.
Goals and objectives
  1. Students should be able to understand the relationship between phenomena and mathematical models and be able to make mathematical models for simple cases.
    The student is also able to explain the background of the models.
  2. Students will understand and be able to apply mathematical analysis techniques to understand the properties of solutions to typical mathematical models.
    Students will also be able to describe them.
  3. The student is able to mathematically analyze typical mathematical models.
    Students are also able to explain them.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 reports Total.
1. 30% 30%
2. 35% 35%
3. 35% 35%
Total. 100% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction
Mathematical models for describing physical and chemical phenomena 		Review calculus, linear algebra probability theory and differential equations 190minutes
2. Mathematical Modeling 2: Mathematical models for describing ecological and social phenomena Review differential equations and review the previous notes and materials. 190minutes
3. Mathematical Modeling 3: Group work on ecosystem models, etc. Review the previous notes and materials. 190minutes
4. Qualitative analysis of nonlinear differential equation systems: fixed points and linearization equations (1D) Review the previous notes and materials. Review Taylor's theorem. 190minutes
5. ・Qualitative analysis of nonlinear differential equation systems: fixed points and linearization equations (multidimensional)
・Analysis of the behavior of solutions of linear models 		Review the previous notes and materials. Review Taylor's theorem for functions of two variables. 190minutes
6. ・Linearization matrices and eigenvalue problems
・Stability of the origin of linearized equations 		Review the previous notes and materials. Review eigenvalue problems for matrices. 190minutes
7. Behavior of solutions around the origin of linearized equations Review the previous notes and materials. 190minutes
8. Analysis of typical mathematical models / Group work Review the previous notes and materials. 190minutes
9. Invariant sets, stable sets, unstable sets, separatrix Review the previous notes and materials. 190minutes
10. Gradient systems, Hamiltonian systems Review the previous notes and materials. 190minutes
11. Limit sets and their invariance, asymptotic behavior of solutions Review the previous notes and materials. 190minutes
12. Lyapunov function Review the previous notes and materials. 190minutes
13. Stability of periodic solutions Review the previous notes and materials. 190minutes
14. ・Differential equation systems with parameters, bifurcation phenomena
・Final assignment (group work) 		Review the previous notes and materials. 190minutes
Total. - - 2660minutes
Evaluation method and criteria
Reports


The achievement of students will be evaluated by exam and reports. If the score is 60% or more, you can pass.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
The Others 授業内、およびScombZ/LMSにてフィードバックを行う。
Textbooks and reference materials
nothing
Prerequisites
calculus, linear algebra and differential equations
Office hours and How to contact professors for questions
  • Thu 12:35-13:05
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
  • Course that cultivates a basic self-management skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Thu Feb 20 04:09:35 JST 2025