HA065000 Analysis III

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HA065000 Subject Classification Specialized Education

Subject Name 解析学III

Subject Name
（Katakana）カイセキガク３

Subject Name in
English Analysis III

Instructor NAITO YUKI

Instructor
(Katakana) ナイトウ　ユウキ

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

Days, Periods, and Classrooms (2T) Tues7-8,Weds7-8：SCI E102

Lesson Style Lecture Lesson Style
(More Details) Face-to-face, Online (on-demand)

Lectures on the blackboard

Credits 2.0 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

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 This course, Analysis III, is provided for understanding the sequence of functions, the series of functions, the continuity of multivariable functions, the derivatives of multivariable functions, and so on.

Class Schedule Lesson1 Pointwise convergence and uniform convergence, I
Lesson2 Pointwise convergence and uniform convergence, II
Lesson3 Differentation and integration of a limit function
Lesson4 Series of functions
Lesson5 Power series, I
Lesson6 Power series, II
Lesson7 Mid-term examination
Lesson8 Topological properties of Euclidean space
Lesson9 Limits of multivariable functions and their continuity, I
Lesson10 Limits of multivariable functions and their continuity, II
Lesson11 Partial differentiation and total differentiation
Lesson12 Chain rule, I
Lesson13 Chain rule, II
Lesson14  Taylor's theorem for multivariable functions,I
Lesson15 Taylor's theorem for multivariable functions, II

Final Lesson : Final examination

Text/Reference
Books,etc. Textbook:
[1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I & II, 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. Text, Handouts, moodle

(More Details) Black board

Learning techniques to be incorporated

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

Requirements The course "Exercises in Analysis III" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis III" and solve many problems in order to understand calculus deeply.

Grading Method Reports and class participation (10%), Midterm examination (40%), Final examination (50%).

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	2026Year	School/Graduate School	School of Science
Lecture Code	HA065000	Subject Classification	Specialized Education
Subject Name	解析学III
Subject Name （Katakana）	カイセキガク３
Subject Name in English	Analysis III
Instructor	NAITO YUKI
Instructor (Katakana)	ナイトウ　ユウキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues7-8,Weds7-8：SCI E102
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face, Online (on-demand)
Lectures on the blackboard
Credits	2.0	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
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	This course, Analysis III, is provided for understanding the sequence of functions, the series of functions, the continuity of multivariable functions, the derivatives of multivariable functions, and so on.
Class Schedule	Lesson1 Pointwise convergence and uniform convergence, I Lesson2 Pointwise convergence and uniform convergence, II Lesson3 Differentation and integration of a limit function Lesson4 Series of functions Lesson5 Power series, I Lesson6 Power series, II Lesson7 Mid-term examination Lesson8 Topological properties of Euclidean space Lesson9 Limits of multivariable functions and their continuity, I Lesson10 Limits of multivariable functions and their continuity, II Lesson11 Partial differentiation and total differentiation Lesson12 Chain rule, I Lesson13 Chain rule, II Lesson14 Taylor's theorem for multivariable functions,I Lesson15 Taylor's theorem for multivariable functions, II Final Lesson : Final examination
Text/Reference Books,etc.	Textbook: [1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I & II, 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.	Text, Handouts, moodle
(More Details)	Black board
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements	The course "Exercises in Analysis III" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis III" and solve many problems in order to understand calculus deeply.
Grading Method	Reports and class participation (10%), Midterm examination (40%), Final examination (50%).
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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