2025Year

First Semester

Applied Analysis

Lecture

Applied Analysis

Z1500010 Applied Analysis

HASEGAWA Kenji

2.0Credits

Tue.1Period

Shinjuku Remote

A) A high degree of specialized expertise　100%
B) The skills to use science and technology　0%
C) The ability to conduct research independently, knowledge pertaining to society and occupations, and sense of ethics required of engineers and researchers　0%
D) Creative skills in specific areas of specialization　0%

The Fourier series, which expresses functions as linear combinations of trigonometric functions, is a powerful analytical tool that has had a significant impact not only in mathematics but also in engineering and information science. In addition to introducing examples of orthogonal function systems other than trigonometric functions, this course will also explain the method of wavelet transformation, which is relatively new in history and can complement the drawbacks of Fourier expansion and Fourier transformation, making it difficult to grasp the local properties of functions. The objectives are as follows:

(1) Understanding the mathematical properties of Fourier expansion and Fourier transformation, and learning how to apply them to differential equations and other areas.
(2) Understanding the general theory of orthogonal function systems and studying classical examples.
(3) Acquiring the ability to apply wavelet transformation to engineering and information science.

Understanding of calculus, integral calculus, and complex functions taught at the undergraduate level is necessary.
It is desirable to be able to use computer algebra systems (such as Matlab, Mathematica, Maxima, etc.) to solve mini-test and report problems.

Support for self-learning using ICT

1. Guidance
2. Fourier Integral and Fourier Series
3. Dirichlet Kernel and Convergence of Fourier Series
4. L2 Norm and Inner Product
5. Mean Convergence
6. Fourier Transform
7. Inversion Formula
8. Delta Function and Heaviside Function
9. Orthogonal Function Systems
10. Legendre Polynomials, Hermite Polynomials, Laguerre Polynomials
11. Continuous Wavelet Transform
12. Discrete Wavelet Transform
13. Scaling Function
14. Meyer Wavelet
15. Daubechies Wavelet
Students will watch the slides and submit their answers to the mini-tests by the deadline. A report assignment will be given at the end of the semester.

The evaluation of grades will be based on a 3:2 ratio between the mini-tests and reports through KU-LMS. However, answers in mini-tests and reports will be considered invalid if students refer no course materials or are suspected that they allow others to copy their answer or reproduce answers from other students or AI-generated response.

The correct answers for the mini-test will be disclosed through KU-LMS. In addition to office hours, the teacher will respond to questions and opinions on Google Meet. The date and time will be discussed via email.

There is no specified textbook. Instead, students will use the PDF files uploaded to KU-LMS for study materials.

Treatises on Fourier analysis, applied analysis, and wavelets.

Monday, 13:00〜14:00(Hachioji:1E-313)

It is an on-demand remote class, chosen as a teaching method deemed more effective than face-to-face interaction. Unless there is a change in instructors, the class format will be maintained going forward.

Not applicable

Electrical Engineering and Electronics Program／Informatics Program