### 2018　Ordinary Differential Equations and Physical Phenomena

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Kanda Manabu  Obara Toru  Nakamura Takashi  Yamashita Yukihiko  Akita Daisuke  Iio Shunji  Tsutsui Hiroaki  Varquez Alvin Christopher Galang
Class Format
Lecture / Exercise
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(S513)  Fri7-8(S513)
Group
-
Course number
TSE.M201
Credits
2
2018
Offered quarter
2Q
Syllabus updated
2018/4/9
Lecture notes updated
-
Language used
Japanese
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.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction of ordinary differential equation - as a tool to understand phenomena can explain the necessity of learning mathematics in engineering and identify basic terminologies
Class 2 First-order ordinary differential equation (1) Can solve some examples of fundamental first-order ordinary differential equation
Class 3 First-order ordinary differential equation (2) Can solve some examples of fundamental first-order ordinary differential equation
Class 4 First-order ordinary differential equation (3) Can solve some examples of fundamental first-order ordinary differential equation
Class 5 Second-order homogeneous linear ordinary differential equation Can solve some examples of second-order homogeneous linear ordinary differential equations
Class 6 Second-order homogeneous linear ordinary differential equation Visualize various phenomena expressed by second-order homogeneous linear ordinary differential equations and obtain the theoretical solutions.
Class 7 Second-order homogeneous linear ordinary differential equation Visualize the theoretical solutions of second-order homogeneous linear ordinary differential equation using PC and obtain the theoretical solutions.
Class 8 Review and midterm examination Review the former half of this class and evaluate the achievement by mid-term examination
Class 9 Second-order inhomogeneous linear ordinary differential equation Can solve some examples of second-order inhomogeneous linear ordinary differential equations
Class 10 Second-order inhomogeneous linear ordinary differential equation Can solve some examples of second-order inhomogeneous linear ordinary differential equations
Class 11 Second-order inhomogeneous linear ordinary differential equation Can solve some examples of second-order inhomogeneous linear ordinary differential equations
Class 12 Numerical solution of ordinary differential equation - Euler method Can numerically solve some examples of ordinary differential equations by Euler method.
Class 13 Numerical solution of ordinary differential equation - Runge-Kutta method Can numerically solve some examples of ordinary differential equations by Runge-Kutta method.
Class 14 Numerical solution of ordinary differential equation - multivariable / n-th order system Can numerically solve some examples of ordinary differential equations of multivariable and n-th order system.
Class 15 Nonlinear ordinary differential equation and Chaos Can obtain the numerical solutions of nonlinear ordinary differential equation using PC and visualize the Chaos phenomena.

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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
• EEE.M221 ： Computation Algorithms and Programming

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### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

tobara[at]lane.iir.titech.ac.jp （Prof. Obara）
htsutsui[at]lane.iir.titech.ac.jp　（Prof. Tsutsui）

### Office hours

Appointment by e-mail is required. 