Hiroshima University Syllabus

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Japanese
Academic Year 2024Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code WSA41000 Subject Classification Specialized Education
Subject Name 数理解析基礎講義A
Subject Name
(Katakana)
スウリカイセキキソコウギエー
Subject Name in
English
Mathematical Analysis A
Instructor TAKIMOTO KAZUHIRO,HIRATA KENTARO,KAMIMOTO SHINGO,KAWASHITA MISHIO
Instructor
(Katakana)
タキモト カズヒロ,ヒラタ ケンタロウ,カミモト シンゴ,カワシタ ミシオ
Campus Higashi-Hiroshima Semester/Term 1st-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 5 : Graduate Basic
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students 1st year of master course
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)
 
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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