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- Common courses
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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Computer Science
- Instructor(s)
- Aonishi Toru
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon7-8(W321) Thr7-8(W321)
- Group
- -
- Course number
- CSC.T351
- Credits
- 2
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- 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 1 |
| Class 9 | Fourier expansion (3) | Properties and Examples 2 |
| Class 10 | Fourier transform (1) | Introduction |
| Class 11 | Fourier transform (2) | Properties and Examples 1 |
| Class 12 | Fourier transform (3) | Properties and Examples 2 |
| Class 13 | Laplace transform (1) | Introduction |
| Class 14 | Laplace transform (2) | Properties and Examples 1 |
| Class 15 | Laplace transform (3) | Properties and Examples 2 |
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 OCW-i.
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.
