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 review calculus, linear algebra and differential equations 190minutes
2. mathematical models in several sciences review differential equations and review the previous notes 190minutes
3. the standard theory of ODE review the previous notes 190minutes
4. simple example for mathematical modeling and its analysis review the previous notes 190minutes
5. linearized problem around the fixed point review the previous notes 190minutes
6. behavior of solutions of linearized problem around the fixed point review the previous notes 190minutes
7. stability of the fixed point review the previous notes 190minutes
8. examples of mathematical analysis for typical nonlinear models review the previous notes 190minutes
9. invariant set, stable set, unstable set and separatrix review the previous notes 190minutes
10. gradient system review the previous notes 190minutes
11. Hamilton system review the previous notes 190minutes
12. Lyapunov function review the previous notes 190minutes
13. stability of periodic solutions review the previous notes 190minutes
14. ODE system with a parameter, the bifurcation theory review the previous notes 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 : Fri Mar 01 04:34:38 JST 2024