2025 (Current Year) Faculty Courses School of Environment and Society Undergraduate major in Transdisciplinary Science and Engineering

Theory of Linear System J

Academic unit or major: Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s): Tatsuya Wakeyama
Class Format: Lecture/Exercise (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 3-4 Mon / 3-4 Thu
Class: J
Course Code: TSE.M203
Number of credits: 110
Course offered: 2025
Offered quarter: 2Q
Syllabus updated: Apr 4, 2025
Language: Japanese

Syllabus

Course overview and goals

The purpose is to learn how to handle complex numbers and their functions, the concept of frequency, and the theory of linear systems necessary for analyzing these systems, which are important in the study of engineering.

Course description and aims

To learn the basics of linear algebra, the function of complex numbers, Fourier transform, Laplace transform, z-transform, theory to model systems and to understand linear circuits and the basis of control theory.

Keywords

Determinant, eigenvalue, eigenvector, function of complex numbers, Cauchy-Riemann equations, Taylor series, Laurant series, pole, Fourier expansion, Fourier transform, Laplace transform, discrete time Fourier transform, discrete Fourier transform, z-transform, continuous time system, discrete time system, controllability, observability, and stability.

Competencies

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

Class flow

Lecture and Practice.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Determinant	To understand how to calculate the determinant
Class 2	Eigenvalue, eigenvector	To understand the calculation using eigenvalue and eigenvector.
Class 3	Sine Wave with Phasor	To understand the calculation using the sine Wave with a Phasor.
Class 4	Fourier expansion	To understand how to calculate the Fourier expansion.
Class 5	Fourier transform	To understand how to calculate the Fourier transform.
Class 6	Laplace transform	To understand how to calculate the Laplace transform.
Class 7	Contour integration, Cauchy-Riemann equations, Cauchy's integral expression	To understand the calculation using the contour integration and Cauchy's integral expression.
Class 8	Residue theorem	To understand the calculation using the residue theorem.
Class 9	Inverse Laplace transform	To understand how to calculate the inverse Laplace transform.
Class 10	Modelling of a continuous-time system	To understand how to model the continuous-time system.
Class 11	Analysis of a continuous-time system	To understand how to analyze the continuous-time system.
Class 12	Transfer function, classical control theory, Bode plot	To understand how to analyze the continuous-time system using a Bode plot.
Class 13	Controllability, observability, and stability.	To understand how to check controllability, observability, and stability.
Class 14	Discrete-time signal, Z-transform	To understand the calculation using the Z-transform.

Study advice (preparation and review)

Students are encouraged to spend approximately 200 minutes for preparation and reviewing class content afterward (including assignments) for each week to enhance effective learning.

Textbook(s)

山下幸彦「線形システム論」朝倉書店, 2013.

Reference books, course materials, etc.

Hwei P. Hsu, "Signals and Systems"

Evaluation methods and criteria

Evaluated based on the weekly reports and the face-to-face final examination.

Related courses

TSE.M201 ： Ordinary Differential Equations and Physical Phenomena

Prerequisites

None in particular

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

wakeyama.t.aa[at]m.titech.ac.jp

Office hours

On the day of the lecture, a question is responded to until 17:00. On the other days, an appointment through e-mail is required. A question is responded to via Zoom.

Other

The syllabus will be changed as needed.