Course title
Mathematical Modeling
Course description
To understand a phenomenon in depth, it is necessary to know not only the data of the phenomenon, but also the rules that generate the data. A mathematical model is a mathematical description of those rules. In addition, to simulate a phenomenon, it is necessary to describe it in a mathematical model.
In this class, students learn the basics of mathematical models limited to differential equations.
Purpose of class
The purpose of this class is to understand mathematical modeling of phenomena and its analytical methods.
In particular, the objectives are mathematical modeling using differential equations, analysis using mathematical theory and computers, and understanding of phenomena by analytical results.
Goals and objectives
1. To be able to understand mathematical models of various phenomena.
2. To be able to use basic mathematical methods for differential equations.
3. To be able to use numerical methods for solving differential equations.
Language
Japanese
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction to Mathematical Models Read through the handouts before class. Review after class. 190minutes
2. Ordinary Differential Equation 1: method of separation of variables and logistic equation Read through the handouts before class. Review after class. 190minutes
3. Ordinary differential equation 2: inhomogeneous linear differential equation of 1st order and RL circuit Read through the handouts before class. Review after class. 190minutes
4. Ordinary differential equation 3: homogeneous linear differential equation of 2nd order and spring-mass system Read through the handouts before class. Review after class. 190minutes
5. Ordinary differential equation 4: inhomogeneous linear differential equation of 2nd order and spring-mass-damper system Read through the handouts before class. Review after class. 190minutes
6. Ordinary Differential Equation 5: system of linear differential equations and eigenvalue Read through the handouts before class. Review after class. 190minutes
7. Midterm examination and its explanation Preparation of midterm examination. 190minutes
8. Partial Differential Equation 1: wave equation and vibration Read through the handouts before class. Review after class. 190minutes
9. Partial differential equation 2: diffusion equation and diffusion of matter Read through the handouts before class. Review after class. 190minutes
10. Partial differential equation 3: laplace and poisson equations Read through the handouts before class. Review after class. 190minutes
11. Numerical solution method 1: finite-difference method Read through the handouts before class. Review after class. 190minutes
12. Numerical Solution 2: finite-difference method by Python Read through the handouts before class. Review after class. 190minutes
13. Design and evaluation of mathematical models Read through the handouts before class. Review after class. 190minutes
14. Final examination and its explanation Preparation of final examination. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Midterm examination Final examination Reports and little examinations Total.
1. 17% 13% 20% 50%
2. 13% 7% 13% 33%
3. 10% 7% 17%
Total. 30% 30% 40% -
Evaluation method and criteria
Midterm examination(30%), Final examination(30%), Reports and Little examinations(40%)
60% if students can understand and solve exercises in the handouts
Textbooks and reference materials
Reference material: 数理モデル入門、齋藤誠慈著、裳華房
Prerequisites
Review Differential and Integral Calculus 1, Linear Algebra 1, Differential and Integral Calculus 2
Office hours and How to contact professors for questions
• 30 minutes after class
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
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 該当しない
Education related SDGs:the Sustainable Development Goals • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE