HA020000 Analysis I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HA020000 Subject Classification Specialized Education

Subject Name 解析学I

Subject Name
（Katakana）カイセキガク１

Subject Name in
English Analysis I

Instructor TAKIMOTO KAZUHIRO

Instructor
(Katakana) タキモト　カズヒロ

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

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

Lesson Style Lecture Lesson Style
(More Details) 　

Lectures on the blackboard

Credits 2.0 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)

Class Objectives
/Class Outline In "Analysis I" and "Analysis II", you will learn fundamental calculus.
This course, Analysis I, is provided for understanding the continuity of real numbers, the limit of sequences, the continuity of functions and so on, rigorously.

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 Mid-term examination
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)

Final lesson : Final examination

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. 　

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

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Lesson1--Lesson15  Review is necessary.

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

Grading Method Reports (15 percents), Midterm examination and Final examination (85 percents).
If I assign some quizes, these scores are 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.

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HA020000	Subject Classification	Specialized Education
Subject Name	解析学I
Subject Name （Katakana）	カイセキガク１
Subject Name in English	Analysis I
Instructor	TAKIMOTO KAZUHIRO
Instructor (Katakana)	タキモト　カズヒロ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues9-10,Thur1-2：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)
Lectures on the blackboard
Credits	2.0	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)
Class Objectives /Class Outline	In "Analysis I" and "Analysis II", you will learn fundamental calculus. This course, Analysis I, is provided for understanding the continuity of real numbers, the limit of sequences, the continuity of functions and so on, rigorously.
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 Mid-term examination 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) Final lesson : Final examination 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.
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson1--Lesson15 Review is necessary.
Requirements	The course "Exercises in Analysis I" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis I" and solve many problems in order to understand calculus deeply.
Grading Method	Reports (15 percents), Midterm examination and Final examination (85 percents). If I assign some quizes, these scores are 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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