Ordinary Differential Equations

Academic unit or major

Undergraduate major in Mechanical Engineering

Instructor(s)

Takahisa Yamazaki / Kazuhiro Yoshida

Class Format

Lecture (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

1-2 Fri (M-374(H131))

Class

-

Course Code

MEC.B211

Number of credits

100

Course offered

2023

Offered quarter

1Q

Syllabus updated

Jul 8, 2025

Language

Japanese

Syllabus

Course overview and goals

This course focuses on the ordinary differential equations used in the analysis of linear systems and nonlinear systems. Topics include 1st order ordinary differential equations, n-th order ordinary differential equations, Fourier series, etc. and also include the functions of elementary solutions of ordinary differential equation. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of mathematical tools widely applicable to linear systems and nonlinear systems in engineering.
This course covers fundamentals of ordinary differential equations as a mathematical knowledge required to solve problems and develop mechanical engineering. By using a mathematical approach such as the differential operation method, students will experience the satisfaction of solving practical problems by using their mathematical knowledge acquired through this course.

Course description and aims

By the end of this course, students will be able to:
1) Explain linear systems and nonlinear systems in ordinary differential equations.
2) Explain the properties of elementary solutions using Wronski determinant.
3) Explain solving method of n-th order ordinary differential equations.
4) Explain the fundamentals of the functions of f general solutions.
5) Apply differential operator to solve problems.

Keywords

Ordinary differential equations, elementary solutions, differential operator, Fourier series, nonlinear ordinary differential equations, perturbation method.

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills
• For applying to mechanical systems, the knowledgs of ordinary differential equations become the foundation of the ability of explanation using mathematics.

Class flow

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purpose.

Course schedule/Objectives

Study advice (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.

Textbook(s)

Kentaro Yano and Shigeru Ishihara: Basic Analysis, Shokabo Co., Ltd, .ISBN: 978-4-7853-1079-0. (Japanese)
Osamu Takenouchi: Differential Equations and Their Application, Saiensu-sha Co., Ltd. Publishers, ISBN: 4-7819-1060-2. (Japanese)

Reference books, course materials, etc.

None required.

Evaluation methods and criteria

Students' knowledge of 1st order ordinary differential equations, n-th order ordinary differential equations, and Fourier series, etc., and their ability to apply them to problems will be assessed.
Examination 65%, exercise problems 35%.

Related courses

• MEC.B213 ： Partial Differential Equations

Prerequisites

Students must have knowledge of calculus.