| Academic Year |
2024Year |
School/Graduate School |
School of Integrated Arts and Sciences Department of Integrated Arts and Sciences |
| Lecture Code |
ANM22001 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析 |
Subject Name
（Katakana） |
スウリカイセキ |
Subject Name in
English |
Mathematical Analysis |
| Instructor |
MIZUMACHI TETSU |
Instructor
(Katakana) |
ミズマチ テツ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
3rd-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Fri1-4：IAS C808 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Blackboard is mainly used. |
| Credits |
2.0 |
Class Hours/Week |
|
Language of Instruction |
B
:
Japanese／English |
| Course Level |
3
:
Undergraduate High-Intermediate
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Fourier Analysis, Partial Differential Equations, Function Spaces |
| 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) | Integrated Arts and Sciences
（Knowledge and Understanding）
・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework.
（Abilities and Skills）
・The ability and skills to specify necessary theories and methods for consideration of issues. |
|---|
Class Objectives
/Class Outline |
The objective of this course is to illustrate applicability of the analysis to various phenomena. The material is Vector Analysis, Fourier Analysis, the Laplace transformation and their applications to ordinary and partial differential equations.
|
| Class Schedule |
lessons 1~2 Laplace transform
lesson 3 The vibrating string and the wave equation
lesson 4 The definition of Fourier series and some examples
lessons 5 Abel summation and Laplace’s equation
lesson 7 Convergence of Fourier series and Parseval's identity
lesson 8 Hilbert spaces
lesson 9 The initial boundary value problem of the heat equation
lesson 10 The initial boundary value problem of the wave equation
lesson 11~12 Definitions and examples of the Fourier transform
lesson 13 Basic properties of the Fourier transform
lesson 14 The Fourier inversion, the Plancherel formula
lesson 15 The Cauchy problem of the heat equation |
Text/Reference
Books,etc. |
References:Fourier Analysis An introduction by Elias M. Stein and Rami Shakarachi
(Princeton Lectures in Analysis, I. Princeton University Press）
|
PC or AV used in
Class,etc. |
|
| (More Details) |
Blackboard |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
It is highly recommended to review as necessary what we learned in courses of Calculus, Complex Analysis and Ordinary Differential Equations. |
| Requirements |
|
| Grading Method |
Based on exams |
| 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. |