| 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 |
WSA43000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析特論Ａ |
Subject Name
（Katakana） |
スウリカイセキトクロンエー |
Subject Name in
English |
Topics in Mathematical Analysis A |
| Instructor |
KAWASHITA MISHIO,HIRATA KENTARO,NAITO YUKI,TAKIMOTO KAZUHIRO |
Instructor
(Katakana) |
カワシタ ミシオ,ヒラタ ケンタロウ,ナイトウ ユウキ,タキモト カズヒロ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Mon3-4,Thur3-4：SCI B305 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Black board is used. Sometime, prints are given. |
| 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 |
|
| Keywords |
|
| 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 |
In the cource, it is explained and demonstrated why knowledge of functional analysis should be needed for studying differential equations. |
| Class Schedule |
lesson1 Finite dimensional vector spaces and Banach spaces
lesson2 Banach spaces (definition, examples, dimension)
lesson3 Initial value problems of ordinary differential equations and functional spaces
lesson4 Linear operators (definition, basic properties, boundedness)
lesson5 Banach spaces consisting of bounded operators
lesson6 Hilbert spaces (definition, examples and orthogonality
lesson7 Orthogonal projections for subspaces in Hilbert spaces
lesson8 Squared integrable Lebesgue spaces
lesson9 Weak derivative and weak form
lesson10 Eigenvalue problem
lesson11 Spectra and resolvents
lesson12 Exponential functions of matrices
lesson13 Linear semigroups
lesson14 Linear Schrodinger equation
lesson15 Elementary non-linear Schrodinger equation
Please note that the lesson plans may be changed depending on the situation. Please understand this in advance. |
Text/Reference
Books,etc. |
Textbooks are not fixed. Any book entitled "Functional Analysis" is good for your textbook if you are interested in it. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Blackboard is only usud. |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Please consider what is the theme on each day's cource. |
| Requirements |
|
| Grading Method |
Grading is mainly based on the report presented in the last part of the course. This is for participants who attend the course at least 2/3 times. For participants not satisfying the rule, the examination should be done and good score is required. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
In Japanese universities it is not customary to bring food or drinks into the classroom unless the instructor gives permission to do so. No Drinking and No Eating in the Classroom, Please! |
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. |