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

EnglishExercises 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 OutlineThe 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

ReviewLesson1--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.