### 2022　Ordinary Differential Equations and Physical Phenomena J

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Academic unit or major
Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Obara Toru  Tsutsui Hiroaki  Nakamura Takashi  Kanda Manabu  Akita Daisuke
Class Format
Lecture / Exercise    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(S011)  Thr1-2(S011)
Group
J
Course number
TSE.M201
Credits
2
2022
Offered quarter
1Q
Syllabus updated
2022/4/4
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

The purpose of this course is to obtain basic knowledge of mathematics for solving various problems related to engineering and science from an interdisciplinary view point. Focusing on ordinary differential equations, the instructor lectures on basic skills for both theoretical and/or numerical solutions.

### Student learning outcomes

By the end of this course, students will be able to:
(1) Judge which ordinary equations should be used to express the phenomena of interest.
(2) Solve the problem using theoretical and numerical methods.
(3) Understand the implications of solutions and interpret the phenomena physically.

### Keywords

ordinary differential equations: theoretical solution: numerical solution: interdisciplinary view point: physical interpretation

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills ✔ Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Lectures mainly consist of classroom teaching with mini-tests. After the end of each chapter, students will do a PC exercise and visualize the solution thereby deepening their physical insight into the phenomena of interest.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction of ordinary differential equations - as a tool to understand phenomena Understand the necessity of learning mathematics in engineering and identify basic terminologies
Class 2 First-order ordinary differential equation Understand various phenomena expressed by first-order ordinary differential equations and obtain theoretical solutions
Class 3 First-order ordinary differential equation Visualize the theoretical solutions of first-order ordinary differential equations using PC and deeply understand the corresponding phenomena
Class 4 Second-order homogeneous linear ordinary differential equation Understand various phenomena expressed by second-order homogeneous linear ordinary differential equations and obtain the theoretical solutions
Class 5 Second-order homogeneous linear ordinary differential equation (PC exercise) Visualize the theoretical solutions of second-order homogeneous linear ordinary differential equation using PC and deeply understand the corresponding phenomena
Class 6 Second-order inhomogeneous linear ordinary differential equation Understand various phenomena expressed by second-order inhomogeneous linear ordinary differential equations and obtain the theoretical solutions
Class 7 Second-order inhomogeneous linear ordinary differential equation (PC exercise) Visualize the theoretical solutions of second-order inhomogeneous linear ordinary differential equation using PC and deeply understand the corresponding phenomena
Class 8 Numerical solution of ordinary differential equation - Euler method Understand the Euler method to solve ordinary differential equations
Class 9 Numerical solution of ordinary differential equation - Runge-Kutta method Understand the Runge-Kutta method to solve ordinary differential equations
Class 10 Numerical solution of ordinary differential equation (PC exercise) Visualize the numerical solutions of linear ordinary differential equation using PC and deeply understand the corresponding phenomena
Class 11 Nonlinear ordinary differential equation and Chaos (Nonlinear spring system) Understand the features of Chaos phenomena expressed by nonlinear ordinary differential equations - Nonlinear spring system
Class 12 Nonlinear ordinary differential equation and Chaos (Food chain and Ecosystem) Understand the features of Chaos phenomena expressed by nonlinear ordinary differential equations - Food chain and Ecosystem
Class 13 Nonlinear ordinary differential equation and Chaos (PC exercise) Visualize the numerical solutions of nonlinear ordinary differential equation using PC and deeply understand the corresponding Chaos phenomena
Class 14 The Butterfly Effect (PC exercise) Visualize the Lorenz Attractor (Chaos phenomena)

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

No english text

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### Assessment criteria and methods

T.B.D. because of COVID-19

### Related courses

• TSE.M202 ： Partial Differential Equations for Science and Engineering
• EEE.M221 ： Computation Algorithms and Programming

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### Office hours

Appointment by e-mail is required.