| Academic Year |
2026Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB281000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析学Ａ |
Subject Name
（Katakana） |
スウリカイセキガクA |
Subject Name in
English |
Mathematical Analysis A |
| Instructor |
KAWASHITA MISHIO |
Instructor
(Katakana) |
カワシタ ミシオ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Weds7-8,Fri5-6：SCI E210 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face, Online (on-demand) |
| 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) | Mathematics
（Knowledge and Understanding）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. |
|---|
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 Uniform boundedness principle
lesson9 Open mapping theorem and closed graph theorem
lesson10 Adjoint spaces
lesson11 Hahn-Banach theorem
lesson12 Second adjoint spaces and reflectivity
lesson13 Adjoint operators
lesson14 Weak convergence
lesson15 Fredholm alternative |
Text/Reference
Books,etc. |
Textbooks are not fixed. |
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. |