HA075000 Exercises in Analysis III

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Science

Lecture Code HA075000 Subject Classification Specialized Education

Subject Name 解析学III演習

Subject Name
（Katakana）カイセキガク３エンシユウ

Subject Name in
English Exercises in Analysis III

Instructor TAKIMOTO KAZUHIRO

Instructor
(Katakana) タキモト　カズヒロ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon3-4,Thur3-4：SCI E104

Lesson Style Seminar Lesson Style
(More Details) Face-to-face

Lectures on the blackboard

Credits 1.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Sophomore (2nd year) students

Keywords Pointwise convergence and uniform convergence, Series of functions and power series, Multivariable function, Partial differential and total differential, Chain rule, Implicit function theorem.

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）
・Understanding classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline The course, Exercises in Analysis III, is given for helping your understanding of the contents of "Analysis III".

Class Schedule Lesson1 Length of a curve
Lesson2 Pointwise convergence and uniform convergence, I (Pointwise convergence and uniform convergence)
Lesson3 Pointwise convergence and uniform convergence, II (The uniform limit of any sequence of continuous functions is
continuous)
Lesson4 Differentation and integration of a limit function
Lesson5 Series of functions
Lesson6 Power series, I (Radius of convergence, Abel's lemma, Limit superior and limit inferior of a sequence)
Lesson7 Power series, II (Term-by-term differentiation, Term-by-term integration, Abel's theorem)
Lesson8 Topological properties of Euclidean space
Lesson9 Limits of multivariable functions and their continuity, I (Defintion and elementary properties)
Lesson10 Limits of multivariable functions and their continuity, II (Intermediate value theorem, Uniform continuity)
Lesson11 Partial differentiation and total differentiation
Lesson12 Chain rule
Lesson13 Taylor's theorem for multivariable functions
Lesson14 Implicit function theorem and inverse function theorem, I (Statement and proof)
Lesson15 Implicit function theorem and inverse function theorem, II (Application)

The proposed plan of the course may be changed in order for the students to deepen their understanding.

Text/Reference
Books,etc. Textbook:
[1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I, Uchida Rokakuho, 2007.

Study-aid books:
[2] Ken-Ichi Shiraiwa, Kaisekigaku-nyumon, Gakujutsu Tosho Shuppan-sha, 1981.
[3] Nobuyuki Suita and Tsunehiko Shimbo, Rikokei-no-Bibunsekibun-gaku, Gakujutsu Tosho Shuppan-sha, 1987.
[4] Koji Kasahara, Bibunsekibun-gaku, Saiensu-sha, 1974.
[5] Kunihiko Kodaira, Kaiseki-nyumon I, Iwanami Shoten, 2003.
[6] Teiji Takagi, Kaiseki-gairon, 3rd Edition, Iwanami Shoten, 1983.

I strongly recommend that you have some books for exercises.

PC or AV used in
Class,etc. Handouts

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

Learning techniques to be incorporated Discussions

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

Requirements It is strongly recommended that you take the course "Analysis III".

Grading Method Mark given in a class (70 percents), Midterm examination and final examination (30 percents).

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	2025Year	School/Graduate School	School of Science
Lecture Code	HA075000	Subject Classification	Specialized Education
Subject Name	解析学III演習
Subject Name （Katakana）	カイセキガク３エンシユウ
Subject Name in English	Exercises in Analysis III
Instructor	TAKIMOTO KAZUHIRO
Instructor (Katakana)	タキモト　カズヒロ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon3-4,Thur3-4：SCI E104
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face
Lectures on the blackboard
Credits	1.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Sophomore (2nd year) students
Keywords	Pointwise convergence and uniform convergence, Series of functions and power series, Multivariable function, Partial differential and total differential, Chain rule, Implicit function theorem.
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）・Understanding classical basic theory which is a base of modern mathematics. Being able to find and explain issues from specific events. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	The course, Exercises in Analysis III, is given for helping your understanding of the contents of "Analysis III".
Class Schedule	Lesson1 Length of a curve Lesson2 Pointwise convergence and uniform convergence, I (Pointwise convergence and uniform convergence) Lesson3 Pointwise convergence and uniform convergence, II (The uniform limit of any sequence of continuous functions is continuous) Lesson4 Differentation and integration of a limit function Lesson5 Series of functions Lesson6 Power series, I (Radius of convergence, Abel's lemma, Limit superior and limit inferior of a sequence) Lesson7 Power series, II (Term-by-term differentiation, Term-by-term integration, Abel's theorem) Lesson8 Topological properties of Euclidean space Lesson9 Limits of multivariable functions and their continuity, I (Defintion and elementary properties) Lesson10 Limits of multivariable functions and their continuity, II (Intermediate value theorem, Uniform continuity) Lesson11 Partial differentiation and total differentiation Lesson12 Chain rule Lesson13 Taylor's theorem for multivariable functions Lesson14 Implicit function theorem and inverse function theorem, I (Statement and proof) Lesson15 Implicit function theorem and inverse function theorem, II (Application) The proposed plan of the course may be changed in order for the students to deepen their understanding.
Text/Reference Books,etc.	Textbook: [1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I, Uchida Rokakuho, 2007. Study-aid books: [2] Ken-Ichi Shiraiwa, Kaisekigaku-nyumon, Gakujutsu Tosho Shuppan-sha, 1981. [3] Nobuyuki Suita and Tsunehiko Shimbo, Rikokei-no-Bibunsekibun-gaku, Gakujutsu Tosho Shuppan-sha, 1987. [4] Koji Kasahara, Bibunsekibun-gaku, Saiensu-sha, 1974. [5] Kunihiko Kodaira, Kaiseki-nyumon I, Iwanami Shoten, 2003. [6] Teiji Takagi, Kaiseki-gairon, 3rd Edition, Iwanami Shoten, 1983. I strongly recommend that you have some books for exercises.
PC or AV used in Class,etc.	Handouts
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated	Discussions
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements	It is strongly recommended that you take the course "Analysis III".
Grading Method	Mark given in a class (70 percents), Midterm examination and final examination (30 percents).
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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