Mathematics for Systems and Control B

Academic unit or major

Undergraduate major in Systems and Control Engineering

Instructor(s)

Hidenori Kosaka

Class Format

Lecture/Exercise (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

5-7 Mon / 5-7 Thu

Class

-

Course Code

SCE.A202

Number of credits

210

Course offered

2024

Offered quarter

3Q

Syllabus updated

Mar 17, 2025

Language

Japanese

Syllabus

Course overview and goals

This course focuses on the solving methods of partial differential equations. Firstly, the classification of partial differential equations and their derivation are presented. Secondly, the separation variables, eigenfunction expansion, Fourier transform, and Laplace transform are presented as the solving methods of parabolic partial differential equation. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of mathematical tools widely applicable to analysis of physical phenomena and design of control systems.

Partial differential equations are used for mathematical expression of various physical phenomena such as electromagnetic field, thermo-flow field, and also for design of control systems. In this course, the solving methods of partial differential equations are explained from the viewpoint of applying them to the engineering problems rather than mathematical rigorousness. The 1-D heat transfer in a rod is taken as an example of solving the partial equation. Students will understand and acquire the fundamentals on solving methods of parabolic partial differential equations for the application of them to engineering issues.

Course description and aims

By the end of this course, students will be able to:
1) Explain the basic classification and properties of partial differential equations.
2) Apply separation variables to solve simple parabolic partial differential equations.
3) Apply eigenfunction expansion to solve simple parabolic partial differential equations.
4) Apply Fourier transform to solve simple parabolic partial differential equations.
5) Apply Laplace transform to solve simple parabolic partial differential equations.

Keywords

parabolic partial differential equation, separation variables, eigenfunction expansion, Fourier transform, Laplace transform

Competencies

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

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 purposes.

Course schedule/Objectives

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Materials will be provided if they are required.

Reference books, course materials, etc.

Reference book: Farlow, Stanley, Partial differential equations for Scientists and Engineers, Dover Publications, Inc.(1996)

Evaluation methods and criteria

Students' knowledge on solving partial differential equations will be assessed by the final examination.

Related courses

• Calculus I
• Calculus II
• Mathematics for Systems and Control A
• Fundamentals of System Science
• System Modeling

Prerequisites

Students are expected to have successfully completed both Calculus I and Calculus II or have equivalent knowledge.