### 2016　Ordinary Differential Equations and Physical Phenomena

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Kanda Manabu  Igashira Masayuki  Obara Toru  Nakamura Takashi  Yamashita Yukihiko  Akita Daisuke  Iio Shunji  Tsutsui Hiroaki  Varquez Alvin Christopher Galang
Course component(s)
Lecture / Exercise
Mode of instruction

Day/Period(Room No.)
Tue7-8(S513)  Fri7-8(S513)
Group
-
Course number
TSE.M201
Credits
2
2016
Offered quarter
3Q
Syllabus updated
2016/4/27
Lecture notes updated
2016/9/22
Language used
English
Access Index ### Course description and aims

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

### Student learning outcomes

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

The course mainly provides classroom lectures with mini-examination. At the end of each chapter, students will do PC exercises and visualize the solutions thereby deepen the physical insight of the phenomena of interest.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction of ordinary differential equation - 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 Review and midterm examination Review the former half of this class and evaluate the achievement by mid-term examination
Class 9 Numerical solution of ordinary differential equation - Euler method Understand the Euler method to solve ordinary differential equations
Class 10 Numerical solution of ordinary differential equation - Runge-Kutta method Understand theRunge-Kutta method to solve ordinary differential equations
Class 11 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 12 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 13 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 14 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 15 Review and Q&A Review and Q&A

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### Assessment criteria and methods

mid-term examination (45%)
term-end examination (45%)
mini-examinations (10%)

### Related courses

• TSE.M202 ： Partial Differential Equations for Science and Engineering

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

Nothing 