HB360000 Topics in Analysis

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Science

Lecture Code HB360000 Subject Classification Specialized Education

Subject Name 解析学特殊講義

Subject Name
（Katakana）カイセキガクトクシュコウギ

Subject Name in
English Topics in Analysis

Instructor KAWASHITA MISHIO

Instructor
(Katakana) カワシタ　ミシオ

Campus Higashi-Hiroshima Semester/Term 4th-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon3-4,Thur3-4：SCI B301

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 4 : Undergraduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Senior students of department of mathematics in faculty of science

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 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

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. The amount and levels of the reports depend on how many times  participants attend the lessons.  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 This course is also provided for graduate students. Hence, you feel that some parts are difficult, however, please do not mind about that, and attend each lesson. Nothing happen before you attend the lessons.

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.

Academic Year	2025Year	School/Graduate School	School of Science
Lecture Code	HB360000	Subject Classification	Specialized Education
Subject Name	解析学特殊講義
Subject Name （Katakana）	カイセキガクトクシュコウギ
Subject Name in English	Topics in Analysis
Instructor	KAWASHITA MISHIO
Instructor (Katakana)	カワシタ　ミシオ
Campus	Higashi-Hiroshima	Semester/Term	4th-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon3-4,Thur3-4：SCI B301
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	4 : Undergraduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Senior students of department of mathematics in faculty of science
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 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
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. The amount and levels of the reports depend on how many times participants attend the lessons. 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	This course is also provided for graduate students. Hence, you feel that some parts are difficult, however, please do not mind about that, and attend each lesson. Nothing happen before you attend the lessons.
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.

Back to syllabus main page