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.
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.
Complex function theory, Frequency domain, Fourier expansion, Fourier transform, Laplace transform
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Students are given exercise problems.
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 |
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
All materials used in class can be found on OCW-i.
Students’ course scores are based on reports (50%) and exams (50%).
It is desirable that students has completed CSC.T362: Numerical Analysis.