### 2019　Theory of Linear System

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Class Format
Lecture / Exercise
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(S513)  Fri1-2(S513)
Group
-
Course number
TSE.M203
Credits
2
2019
Offered quarter
3Q
Syllabus updated
2019/4/5
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

The purpose of this course 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.

### Student learning outcomes

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 that will be developed

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

### Class flow

Lecture and Practice

### Course schedule/Required learning

Course schedule Required learning
Class 1 Determinant Calculation of determinant
Class 2 Eigen value and eigen vector Calculation with eigen value and eigen vector
Class 3 Function of complex numbers Calculation with functions of complex numbers
Class 4 Analytic functions and Cauchy-Riemann equation Calculation with analytic functions and Cauchy-Riemann equation
Class 5 Integral of function of complex numbers Calculation with integral of function of complex numbers
Class 6 Taylor series, Laurent series, pole, singular point, and residue equation Calculation with Taylor series, Laurent series, pole, singular point, and residue equation
Class 7 Fourier series Calculation of Fourier series
Class 8 Fourier transform Calculation of Fourier transform
Class 9 Laplace transform Calculation of Laplace transform
Class 10 Laplace inverse transform Calculation of Laplace inverse transform
Class 11 Modeling of continuous time system Modeling a continuous time system
Class 12 Analysis of continuous time system Analysis of a continuous time system
Class 13 Feedback control Calculation of Feedback control
Class 14 Controllability, observability, and stability Judgement of controllability, observability, and stability
Class 15 Transformation of discrete time function Calculation of transformation of discrete time function

### Textbook(s)

Hwei P. Hsu, "Signals and Systems"

### Reference books, course materials, etc.

None in particular

### Assessment criteria and methods

Evaluated based on the final examination and reports.

### Related courses

• TSE.M201 ： Ordinary Differential Equations and Physical Phenomena

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular

### Other

Syllabus will be changed at any time.