| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA41000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析基礎講義Ａ |
Subject Name
（Katakana） |
スウリカイセキキソコウギエー |
Subject Name in
English |
Mathematical Analysis A |
| Instructor |
TAKIMOTO KAZUHIRO,HIRATA KENTARO,NAITO YUKI,KAWASHITA MISHIO |
Instructor
(Katakana) |
タキモト カズヒロ,ヒラタ ケンタロウ,ナイトウ ユウキ,カワシタ ミシオ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Tues7-8,Thur3-4：SCI B301 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face, Online (on-demand) |
| Lectures on the blackboard |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
B
:
Japanese／English |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
1st year of master course |
| Keywords |
Function space, Fourier transform, Distribution. |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
We learn the basic theory of Fourier transform and distributions. |
| Class Schedule |
Lesson1 Introduction (What Fourier transform and distributions are all about?)
Lesson2 Fourier transform, I (Function spaces)
Lesson3 Fourier transform, II (Fourier transform for integrable functions)
Lesson4 Fourier transform, III (Convolution & rapidly decreasing function)
Lesson5 Fourier transform, IV (Inversion theorem)
Lesson6 Fourier transform, V (Properties of Fourier transform)
Lesson7 Fourier transform, VI (Fourier tranform for L^2 functions & Plancherel's theorem)
Lesson8 Fourier transform, VII (Some applications)
Lesson9 Distributions, I (Preliminaries & definition)
Lesson10 Distributions, II (Operations for distributions)
Lesson11 Distributions, III (Convergence of the sequence of distributions)
Lesson12 Distributions, IV (Distributions with compact support)
Lesson13 Fourier transform of distributions, I (Definition & example)
Lesson14 Fourier transform of distributions, II (Properties of Fourier trnasform & tempered distributions)
Lesson15 Fourier transform of distributions, III (Sobolev space)
Final lesson : Final examination |
Text/Reference
Books,etc. |
Study-aid books:
[1] Shigetoshi Kuroda, Kansu Kaiseki (Functional Analysis), Kyoritsu Shuppan, 1980.
[2] Shu Nakamura, Fourier Kaiseki (Fourier Analysis), Asakura Publishing, 2003.
[3] Hitoshi Arai, Fourier Kaisekigaku (Fourier Analysis), Asakura Publishing, 2003.
[4] Hitoshi Arai, Shin Fourier Kaiseki to Kansu Kaiseki (Fourier Analysis and Functional Analysis), Baifukan, 2010. |
PC or AV used in
Class,etc. |
Handouts, Visual Materials |
| (More Details) |
I will hand out some documentations if necessary. |
| Learning techniques to be incorporated |
Post-class Report |
Suggestions on
Preparation and
Review |
Lesson 1--Lesson 15 Review is necessary. |
| Requirements |
|
| Grading Method |
Usual performance score (25 percents), reports (25 percents) and final examination (50 percents). |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |