HA500000 Exercises in Analysis I

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Science

Lecture Code HA500000 Subject Classification Specialized Education

Subject Name 解析学I演習

Subject Name
（Katakana）カイセキガク１エンシュウ

Subject Name in
English Exercises in Analysis I

Instructor NAITO YUKI,SUKENAGA MASAYUKI

Instructor
(Katakana) ナイトウ　ユウキ,スケナガ　マサユキ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Tues9-10,Thur1-2：SCI E209,SCI E211

Lesson Style Seminar Lesson Style
(More Details) Face-to-face, Online (simultaneous interactive)

Exercises and presentations on the blackboard
This class is given face-to-face or online depending on the situation.

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

Course Level 1 : Undergraduate Introductory

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Freshman (1st year) students

Keywords Continuity of real numbers, Convergence and divergence of sequences, Series, Continuity of functions.

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 The course, Exercises in Analysis I, is given for helping your understanding of the contents of "Analysis I".

Class Schedule Lesson1 Continuity of real numbers, I : Supremum, Infimum, Maximum, Minimum
Lesson2 Continuity of real numbers, II : Continuity of real numbers
Lesson3 Sequences, I : Sequences and limits
Lesson4 Sequences, II : Properties of limits
Lesson5 Sequences, III : Divergence to infinity
Lesson6 Sequences, IV : Cauchy sequences
Lesson7 Limits of functions
Lesson8 Review
Lesson9 Limits of functions: fundamental properties
Lesson10 Limits of functions and limits of sequences
Lesson11 Properties of continuous functions
Lesson12  Series, I : Convergence, Divergence
Lesson13 Series, II : Radius of convergence
Lesson14  Series, III : Absolute convergence, Conditional convergence
Lesson15 Inverse trigonometric functions

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.
[7] Shigetoshi Kuroda, Bibunsekibun, Kyoritsu Shuppan, 2002.
[8] Ichiro Tajima, Ipushiron-Delta, Kyoritsu Shuppan, 1978.
[9] Tadayuki Hara, Hideaki Matsunaga, Ipushiron-Delta Ronpou Kanzen Kouryaku, Kyoritsu Shuppan, 2011.

I strongly recommend that you have some books for exercises.

PC or AV used in
Class,etc. Handouts, Microsoft Teams

(More Details) Black board

Learning techniques to be incorporated Discussions, Quizzes/ Quiz format, Post-class Report

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

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

Grading Method Presentation in a class (40%), Report and Quiz (10%), Midterm examination and final examinations (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	2025Year	School/Graduate School	School of Science
Lecture Code	HA500000	Subject Classification	Specialized Education
Subject Name	解析学I演習
Subject Name （Katakana）	カイセキガク１エンシュウ
Subject Name in English	Exercises in Analysis I
Instructor	NAITO YUKI,SUKENAGA MASAYUKI
Instructor (Katakana)	ナイトウ　ユウキ,スケナガ　マサユキ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues9-10,Thur1-2：SCI E209,SCI E211
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face, Online (simultaneous interactive)
Exercises and presentations on the blackboard This class is given face-to-face or online depending on the situation.
Credits	1.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	1 : Undergraduate Introductory
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Freshman (1st year) students
Keywords	Continuity of real numbers, Convergence and divergence of sequences, Series, Continuity of functions.
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	The course, Exercises in Analysis I, is given for helping your understanding of the contents of "Analysis I".
Class Schedule	Lesson1 Continuity of real numbers, I : Supremum, Infimum, Maximum, Minimum Lesson2 Continuity of real numbers, II : Continuity of real numbers Lesson3 Sequences, I : Sequences and limits Lesson4 Sequences, II : Properties of limits Lesson5 Sequences, III : Divergence to infinity Lesson6 Sequences, IV : Cauchy sequences Lesson7 Limits of functions Lesson8 Review Lesson9 Limits of functions: fundamental properties Lesson10 Limits of functions and limits of sequences Lesson11 Properties of continuous functions Lesson12 Series, I : Convergence, Divergence Lesson13 Series, II : Radius of convergence Lesson14 Series, III : Absolute convergence, Conditional convergence Lesson15 Inverse trigonometric functions
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. [7] Shigetoshi Kuroda, Bibunsekibun, Kyoritsu Shuppan, 2002. [8] Ichiro Tajima, Ipushiron-Delta, Kyoritsu Shuppan, 1978. [9] Tadayuki Hara, Hideaki Matsunaga, Ipushiron-Delta Ronpou Kanzen Kouryaku, Kyoritsu Shuppan, 2011. I strongly recommend that you have some books for exercises.
PC or AV used in Class,etc.	Handouts, Microsoft Teams
(More Details)	Black board
Learning techniques to be incorporated	Discussions, Quizzes/ Quiz format, Post-class Report
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements	It is strongly recommended that you take the course "Analysis I".
Grading Method	Presentation in a class (40%), Report and Quiz (10%), Midterm examination and final examinations (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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