HA035000 Analysis II

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HA035000 Subject Classification Specialized Education

Subject Name 解析学II

Subject Name
（Katakana）カイセキガク２

Subject Name in
English 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) Mon3-4,Weds3-4：SCI E209

Lesson Style Lecture Lesson Style
(More Details) Face-to-face, Online (on-demand)

Lectures on the blackboard

Credits 2.0 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 In "Analysis I" and "Analysis II", you will learn fundamental concepts of calculus.
This course, Analysis II, is designed to help you rigorously understand Riemann integrals, Taylor's theorem and other topics.

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 funtions, irratinoal functions and exponential functions)
Lesson8 Mid-term examination
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

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. Handouts, Visual Materials, moodle

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

Learning techniques to be incorporated Post-class Report

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

Requirements The course "Exercises in Analysis II" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis II" 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	2026Year	School/Graduate School	School of Science
Lecture Code	HA035000	Subject Classification	Specialized Education
Subject Name	解析学II
Subject Name （Katakana）	カイセキガク２
Subject Name in English	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) Mon3-4,Weds3-4：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face, Online (on-demand)
Lectures on the blackboard
Credits	2.0	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	In "Analysis I" and "Analysis II", you will learn fundamental concepts of calculus. This course, Analysis II, is designed to help you rigorously understand Riemann integrals, Taylor's theorem and other topics.
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 funtions, irratinoal functions and exponential functions) Lesson8 Mid-term examination 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 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.	Handouts, Visual Materials, moodle
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated	Post-class Report
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements	The course "Exercises in Analysis II" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis II" 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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