HB281000 Mathematical Analysis A

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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 TAKIMOTO KAZUHIRO

Instructor
(Katakana) タキモト　カズヒロ

Campus Higashi-Hiroshima Semester/Term 4th-Year,  First Semester,  1Term

Days, Periods, and Classrooms (1T) Tues7-8,Thur3-4：SCI B301

Lesson Style Lecture Lesson Style
(More Details) 　

Lectures on the blackboard

Credits 2.0 Class Hours/Week 　 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 (4th year) students

Keywords Banach space, Hilbert space, L^p space, Bounded linear operator, Uniform boundedness principle, Linear functional, Compact operator.

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 We learn the basic theory of functional analysis, such as Banach spaces, Hilbert spaces and bounded linear operators.

Class Schedule Lesson1 Normed space snd completeness
Lesson2 Function spaces, I (C(I), B^m(I), C_0(R^n), etc.)
Lesson3 Function spaces, II (Lebesgue space)
Lesson4 Banach spaces, I (Product space, Quotient space, Completion)
Lesson5 Banach spaces II (Finite dimensional normed space is a Banach space)
Lesson6 Hilbert spaces, I (Schwarz' inequality, orthogonal complement)
Lesson7 Hilbert spaces, II (Complete orthonormal system, Schmidt orthonormalization)
Lesson8 Bounded linear operators
Lesson9 Uniform boundedness principle
Lesson10 Open mapping theorem
Lesson11 Bounded functionals and conjugate spaces
Lesson12 Hahn-Banach theorem
Lesson13 Weak convergence and weak* convergence, I (Definition & example)
Lesson14 Weak convergence and weak* convergence, II (Closed unit ball in a reflexive Banach space is weakly sequentially compact)
Lesson15 Compact operator

Final Lesson : Final examination

Text/Reference
Books,etc. Study-aid books:
[1] Shigetoshi Kuroda, Kansu Kaiseki (Functional Analysis), Kyoritsu Shuppan, 1980.
[2] Kyuya Masuda, Kansu Kaiseki (Functional Analysis), Shokabo, 1994.
[3] Hiroshi Fujita, Shigetoshi Kuroda and Seizo Ito, Kansu Kaiseki (Functional Analysis), Iwanami Shoten, 1991.
[4] Isao Miyadera, Kansu Kaiseki (Functional Analysis), Rikogakusha, 1972.

PC or AV used in
Class,etc. 　

(More Details) I will hand out some documentations if necessary.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Lesson 1--Lesson 15  Review is necessary.

Requirements

Grading Method Class participation (25 percents), reports (25 percents) and final examination (50 percents).
If I assign mid-term examination, its score is also considered.

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.

Academic Year	2024Year	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	TAKIMOTO KAZUHIRO
Instructor (Katakana)	タキモト　カズヒロ
Campus	Higashi-Hiroshima	Semester/Term	4th-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Tues7-8,Thur3-4：SCI B301
Lesson Style	Lecture	Lesson Style (More Details)
Lectures on the blackboard
Credits	2.0	Class Hours/Week		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 (4th year) students
Keywords	Banach space, Hilbert space, L^p space, Bounded linear operator, Uniform boundedness principle, Linear functional, Compact operator.
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	We learn the basic theory of functional analysis, such as Banach spaces, Hilbert spaces and bounded linear operators.
Class Schedule	Lesson1 Normed space snd completeness Lesson2 Function spaces, I (C(I), B^m(I), C_0(R^n), etc.) Lesson3 Function spaces, II (Lebesgue space) Lesson4 Banach spaces, I (Product space, Quotient space, Completion) Lesson5 Banach spaces II (Finite dimensional normed space is a Banach space) Lesson6 Hilbert spaces, I (Schwarz' inequality, orthogonal complement) Lesson7 Hilbert spaces, II (Complete orthonormal system, Schmidt orthonormalization) Lesson8 Bounded linear operators Lesson9 Uniform boundedness principle Lesson10 Open mapping theorem Lesson11 Bounded functionals and conjugate spaces Lesson12 Hahn-Banach theorem Lesson13 Weak convergence and weak* convergence, I (Definition & example) Lesson14 Weak convergence and weak* convergence, II (Closed unit ball in a reflexive Banach space is weakly sequentially compact) Lesson15 Compact operator Final Lesson : Final examination
Text/Reference Books,etc.	Study-aid books: [1] Shigetoshi Kuroda, Kansu Kaiseki (Functional Analysis), Kyoritsu Shuppan, 1980. [2] Kyuya Masuda, Kansu Kaiseki (Functional Analysis), Shokabo, 1994. [3] Hiroshi Fujita, Shigetoshi Kuroda and Seizo Ito, Kansu Kaiseki (Functional Analysis), Iwanami Shoten, 1991. [4] Isao Miyadera, Kansu Kaiseki (Functional Analysis), Rikogakusha, 1972.
PC or AV used in Class,etc.
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements
Grading Method	Class participation (25 percents), reports (25 percents) and final examination (50 percents). If I assign mid-term examination, its score is also considered.
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.

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