HA500000 Exercises in Analysis I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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 TAKIMOTO KAZUHIRO,KOREEDA YOSHIMUNE

Instructor
(Katakana) タキモト　カズヒロ,コレエダ　ヨシムネ

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

Days, Periods, and Classrooms (2T) Weds5-6,Fri5-6：SCI E209,SCI E211

Lesson Style Seminar Lesson Style
(More Details) 　

Exercises and presentations on the blackboard

Credits 1.0 Class Hours/Week 　 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, Derivative.

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 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 (Axiom of the continutity of real numbers)
Lesson3 Sequences, I (Defintion of the limit, convegence and divergence)
Lesson4 Sequences, II (Elementary properties)
Lesson5 Sequences, III (Cauchy sequence, Completeness of real numbers)
Lesson6 Series, I (Definition of convergence and divergence)
Lesson7 Series, II (Method of convergence criteria)
Lesson8 Series, III (Alternating series, Absolute convergence and conditional convergence)
Lesson9 Review
Lesson10 Limits of functions and continuous functions, I (Defintion and elementary properties)
Lesson11 Limits of functions and continuous functions, II (Extreme value theorem, Intermediate value theorem)
Lesson12 Limits of functions and continuous functions, III (Continuity of inverse function, Uniform continuity)
Lesson13 Derivatives, I (Defintion and elementary properties)
Lesson14 Derivatives, II (Derivative of composite function, Derivative of inverse function)
Lesson15 Derivatives, III (Mean-value theorem)

Some quizes and some reports may be assigned.

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. 　

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

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Lesson1--Lesson15  Preparation and review are necessary.

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

Grading Method Mark given in a class (65 percents), Midterm examination and final examinations (35 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	2024Year	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	TAKIMOTO KAZUHIRO,KOREEDA YOSHIMUNE
Instructor (Katakana)	タキモト　カズヒロ,コレエダ　ヨシムネ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Weds5-6,Fri5-6：SCI E209,SCI E211
Lesson Style	Seminar	Lesson Style (More Details)
Exercises and presentations on the blackboard
Credits	1.0	Class Hours/Week		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, Derivative.
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 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 (Axiom of the continutity of real numbers) Lesson3 Sequences, I (Defintion of the limit, convegence and divergence) Lesson4 Sequences, II (Elementary properties) Lesson5 Sequences, III (Cauchy sequence, Completeness of real numbers) Lesson6 Series, I (Definition of convergence and divergence) Lesson7 Series, II (Method of convergence criteria) Lesson8 Series, III (Alternating series, Absolute convergence and conditional convergence) Lesson9 Review Lesson10 Limits of functions and continuous functions, I (Defintion and elementary properties) Lesson11 Limits of functions and continuous functions, II (Extreme value theorem, Intermediate value theorem) Lesson12 Limits of functions and continuous functions, III (Continuity of inverse function, Uniform continuity) Lesson13 Derivatives, I (Defintion and elementary properties) Lesson14 Derivatives, II (Derivative of composite function, Derivative of inverse function) Lesson15 Derivatives, III (Mean-value theorem) Some quizes and some reports may be assigned.
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.
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson1--Lesson15 Preparation and review are necessary.
Requirements	It is strongly recommended that you take the course "Analysis I".
Grading Method	Mark given in a class (65 percents), Midterm examination and final examinations (35 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.

Back to syllabus main page