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.
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.
Ordinary differential equations, elementary solutions, differential operator, Fourier series, nonlinear ordinary differential equations, perturbation method.
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | - | ✔ | - | ✔ |
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 | Required learning | |
---|---|---|
Class 1 | Introduction of ordinery differntial equations. 1st order ordinery differntial equations | Understand elementary solutions, particular solutions, and general solutions. |
Class 2 | n-th order ordinery differential equations | Understand general solutions and Wronski determinant. |
Class 3 | n-th order ordinery differential equations | Understand differential operator and variation of parameters. |
Class 4 | Similutanious ordinary differential equations | Understand eigenvalue. |
Class 5 | Solving by series | Understand solving by series. |
Class 6 | Nonlinear ordinary differential equations, orthogonal functions | Understand perturbation method and Bessel function. |
Class 7 | Fourier series | Understand Fourier series |
Class 8 | Examination and summary | Test level of understanding and summary. |
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)
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.
Exam 80%, exercise problems 20%.
Students must have knowledge of calculus.