### 2022　System Analysis

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Instructor(s)
Aonishi Toru
Class Format
Lecture    (HyFlex)
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(S011)  Thr7-8(S011)
Group
-
Course number
CSC.T351
Credits
2
2022
Offered quarter
2Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

This lecture covers the basic mathematical knowledge required for analyzing dynamical systems.
First, the complex function theory is introduced as preparation to the frequency-domain analysis.
Next, Fourier expansion, Fourier transform and Laplace transform are explained.

### Student learning outcomes

The aim of this lecture to make students acquire the basic mathematical knowledge required in four courses related to dynamical systems in this department. At the end of this course, students will acquire mathematical skills for analyzing dynamical systems through studying Fourier expansion, Fourier transform and Laplace transform.

### Keywords

Complex function theory, Frequency domain, Fourier expansion, Fourier transform, Laplace transform

### Competencies that will be developed

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

### Class flow

Students are given exercise problems.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Complex function theory (1) Properties of complex number and complex function 1
Class 2 Complex function theory (2) Properties of complex number and complex function 2
Class 3 Complex function theory (3) Derivatives of complex functions
Class 4 Complex function theory (4) Integrals of complex functions 1
Class 5 Complex function theory (5) Integrals of complex functions 2
Class 6 Complex function theory (6) Series expansions of complex functions
Class 7 Fourier expansion (1) Introduction
Class 8 Fourier expansion (2) Properties and Examples
Class 9 Fourier transform (1) Introduction
Class 10 Fourier transform (2) Properties and Examples 1
Class 11 Fourier transform (3) Properties and Examples 2
Class 12 Laplace transform (1) Introduction
Class 13 Laplace transform (2) Properties and Examples 1
Class 14 Laplace transform (3) Properties and Examples 2

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

Hiroshi, Usui. Foundation of Applied analysis- Complex function theory・Fourier analysis・Laplace transform. Coronasha. ISBN-10: 4339060666
Yo, Kenro. Foundation of Fourier analysis and Laplace transform for system analysis. Coronasha. ISBN-10: 433906095X

### Reference books, course materials, etc.

All materials used in class can be found on T2SCHOLA.

### Assessment criteria and methods

Students’ course scores are based on reports (50%) and exams (50%).

### Related courses

• CSC.T373 ： Dynamical Systems
• CSC.T374 ： Control Systems
• CSC.T362 ： Numerical Analysis
• CSC.T342 ： Problem Solving and Decision Making

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

It is desirable that students has completed CSC.T362: Numerical Analysis. 