2024 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
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 17, 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 | Function of complex numbers, series, derivative | To understand the calculation using the function of complex numbers. |
| Class 4 | Domain, regular, Cauchy-Riemann equations | To understand the calculation using the domain, regular, and the Cauchy-Riemann equations. |
| Class 5 | Contour integration, Cauchy's integral expression | To understand the calculation using the contour integration and Cauchy's integral expression. |
| Class 6 | Taylor series, Laurent series, pole, singular point, Residue theorem | To understand the calculation using the Taylor series, Laurent series, pole, singular point, and residue theorem. |
| Class 7 | Fourier expansion | To understand how to calculate the Fourier expansion. |
| Class 8 | Fourier transform | To understand how to calculate the Fourier transform. |
| Class 9 | Laplace transform | To understand how to calculate the Laplace transform. |
| Class 10 | Inverse Laplace transform | To understand how to calculate the inverse Laplace transform. |
| Class 11 | Modelling of continuous-time system | To understand how to model the continuous-time system. |
| Class 12 | Analysis of continuous-time system | To understand how to analyze the continuous-time system. |
| Class 13 | Feedback control | To understand how to calculate the feedback control. |
| Class 14 | Controllability, observability, and stability. | To understand how to check controllability, observability, and stability. |
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.