HA510000 Exercises in Analysis II

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HA510000 Subject Classification Specialized Education

Subject Name 解析学II演習

Subject Name
（Katakana）カイセキガクニエンシュウ

Subject Name in
English Exercises in Analysis II

Instructor TAKIMOTO KAZUHIRO

Instructor
(Katakana) タキモト　カズヒロ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  4Term

Days, Periods, and Classrooms (4T) Tues9-10,Fri3-4：SCI E209

Lesson Style Seminar Lesson Style
(More Details) Face-to-face

Exercises and presentations on the blackboard

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 Riemann integrals, Fundamental theorem of calculus, Taylor's theorem, Local maximum and local minimum of a function, Improper integrals, Length of a curve, Differential equations.

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 II, is given for helping your understanding of the contents of "Analysis II".

Class Schedule Lesson1 Derivatives, IV (Higher-order derivatives, Leibniz' theorem)
Lesson2 Riemann integrals, I (Definition of the definite integral)
Lesson3 Riemann integrals, II (A continuous function must be integrable)
Lesson4 Properties of definite integrals
Lesson5 Fundamental theorem of calculus
Lesson6 Calculus of definite integrals and indefinite integrals, I (Integrals of rational functions)
Lesson7 Calculus of definite integrals and indefinite integrals, II (Integrals of trigonometric functions, irrational functions and exponential functions)
Lesson8 Review
Lesson9 Taylor's theorem, I (Statement and proof)
Lesson10 Taylor's theorem, II (Landau symbol and Taylor series expansion)
Lesson11 Local maximum and local minimum of a function, a convex function
Lesson12 Improper integrals, I (Definitions and properties)
Lesson13 Improper integrals, II (Convergence criterion of improper integrals, Beta function & Gamma function)
Lesson14 Length of a curve
Lesson15 Quadrature of differential equations

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. Handouts, Microsoft Teams, moodle

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

Learning techniques to be incorporated Discussions, Quizzes/ Quiz format

Suggestions on
Preparation and
Review Lesson 1--Lesson 15  Preparation and review are necessary.

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

Grading Method Mark given in a class (70 percents), Midterm examination and final examination (30 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	2026Year	School/Graduate School	School of Science
Lecture Code	HA510000	Subject Classification	Specialized Education
Subject Name	解析学II演習
Subject Name （Katakana）	カイセキガクニエンシュウ
Subject Name in English	Exercises in Analysis II
Instructor	TAKIMOTO KAZUHIRO
Instructor (Katakana)	タキモト　カズヒロ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues9-10,Fri3-4：SCI E209
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face
Exercises and presentations on the blackboard
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	Riemann integrals, Fundamental theorem of calculus, Taylor's theorem, Local maximum and local minimum of a function, Improper integrals, Length of a curve, Differential equations.
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 II, is given for helping your understanding of the contents of "Analysis II".
Class Schedule	Lesson1 Derivatives, IV (Higher-order derivatives, Leibniz' theorem) Lesson2 Riemann integrals, I (Definition of the definite integral) Lesson3 Riemann integrals, II (A continuous function must be integrable) Lesson4 Properties of definite integrals Lesson5 Fundamental theorem of calculus Lesson6 Calculus of definite integrals and indefinite integrals, I (Integrals of rational functions) Lesson7 Calculus of definite integrals and indefinite integrals, II (Integrals of trigonometric functions, irrational functions and exponential functions) Lesson8 Review Lesson9 Taylor's theorem, I (Statement and proof) Lesson10 Taylor's theorem, II (Landau symbol and Taylor series expansion) Lesson11 Local maximum and local minimum of a function, a convex function Lesson12 Improper integrals, I (Definitions and properties) Lesson13 Improper integrals, II (Convergence criterion of improper integrals, Beta function & Gamma function) Lesson14 Length of a curve Lesson15 Quadrature of differential equations 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.	Handouts, Microsoft Teams, moodle
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated	Discussions, Quizzes/ Quiz format
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Preparation and review are necessary.
Requirements	It is strongly recommended that you take the course "Analysis II".
Grading Method	Mark given in a class (70 percents), Midterm examination and final examination (30 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.

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