[前へ戻る]
   

 授業科目
 Course Title
解析学特論
Topics in Analysis 
 担当者
 Instructor
講師   瀬戸 道生  後学期 月曜日4時限
 単 位
 Credit
2

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^2-geometry
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 e-mail.

 

参考書 Book (s) for Reference
H. Dym and H. P. Mckean,,FOURIER SERIES AND INTEGRALS,Academic Press

 
 
 
[前へ戻る]