


関連するディプロマポリシー Related Diploma Policy

時代の課題と社会の要請に応えた専門的知識と技能/Expert knowledge and skills to address the issues of the age and the demands of society



到達目標 Target to be Reached

After the course, the students are expected to be able to:
understand the basic concept of Fourier series and integrals,
use and apply the famous formulas (Fourier inversion formula, Parseval's formula, Plancherel's formula, etc.),
understand the role of the theory of Lebesgue integral in Fourier analysis.


授業内容 Course Content

Fourier analysis is not only useful in many fields,
but also interesting as a theory in mathematics.
The pourpose of this lecture is to introduce its basic theory and applications,
and also this course is intended to be support to understand functional analysis.
The course covers the following topics:
Fourier series, Dirichlet's theorem, heat equation on the circle, Fejer's theorem, L^2 space, Parseval formula,
Fourier integrals, Schwartz class, inversion formula, heat equation on the real line, Plancherel's theorem,
and various applications.


授業計画 Course Planning

01. Introduction
02. Fourier coefficients
03. L^2geometry
04. Dirichlet kernel
05. Dirichlet's theorem
06. Heat equation on the circle
07. Fejer's theorem
08. Parseval's formula
09. Fourier integrals
10. Schwartz class
11. Fourier inversion formula
12. Heat equation on the real line
13. Plancherel's theorem
14. Various applications
Lecture notes will be given in the first lecture.
Homework will be given in ``almost every" lecture.
Your solutions to the assigned homework will be graded and returned to you.


授業運営 Course Management

Lecture


評価方法 Evaluation Method

The final grade will be based on the homework.


オフィスアワー Office Hour (s)

The students may ask questions by email.



参考書 Book (s) for Reference

H. Dym and H. P. Mckean,,FOURIER SERIES AND INTEGRALS,Academic Press


