HA035000 Analysis ＩＩ

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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 HIRATA KENTARO

Instructor
(Katakana) ヒラタ　ケンタロウ

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

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

Lesson Style Lecture Lesson Style
(More Details) 　

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 in Department of Mathematics

Keywords Taylor's theorem, Extremum, Riemann integrals, Fundamental theorem of calculus, Improper integrals.

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 This course, Analysis II, is provided for understanding Riemann integral, Taylor's theorem and so on, rigorously.

Class Schedule Lesson1 Higher-order derivatives, Leibniz' theorem
Lesson2 Taylor's theorem
Lesson3 Taylor series, Landau symbol
Lesson4 Convex function and extremum
Lesson5 l'Hopital's theorem
Lesson6 Definition of Riemann's integral
Lesson7 Integrability of continuous functions
Lesson8 Properties of definite integrals
Lesson9 Mid-term examination
Lesson10 Fundamental theorem of calculus
Lesson11 Integration by parts, Integration by substitution
Lesson12 Integrals of rational functions
Lesson13 Integrals of trigonometric funtions, irratinoal functions and exponential functions
Lesson14 Definitions and properties of improper integrals
Lesson15 Convergence criterion of improper integrals, Beta function and Gamma function

Mid-term exam. and final exam. will be given.

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.
[7] Shigetoshi Kuroda, Bibunsekibun, Kyoritsu Shuppan, 2002.
[8] Ichiro Tajima, Ipushiron-Delta, Kyoritsu Shuppan, 1978.
[9] Tadayuki Hara, Hideaki Matsunaga, Ipushiron-Delta Ronpou Kanzen Kouryaku, Kyoritsu Shuppan, 2011.

I strongly recommend that you have some books for exercises.

PC or AV used in
Class,etc. 　

(More Details) Black board

Learning techniques to be incorporated 　

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 Midterm examination (40%), Final examination (50%), Quiz (10%).

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	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	HIRATA KENTARO
Instructor (Katakana)	ヒラタ　ケンタロウ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues9-10,Fri3-4：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)

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 in Department of Mathematics
Keywords	Taylor's theorem, Extremum, Riemann integrals, Fundamental theorem of calculus, Improper integrals.
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	This course, Analysis II, is provided for understanding Riemann integral, Taylor's theorem and so on, rigorously.
Class Schedule	Lesson1 Higher-order derivatives, Leibniz' theorem Lesson2 Taylor's theorem Lesson3 Taylor series, Landau symbol Lesson4 Convex function and extremum Lesson5 l'Hopital's theorem Lesson6 Definition of Riemann's integral Lesson7 Integrability of continuous functions Lesson8 Properties of definite integrals Lesson9 Mid-term examination Lesson10 Fundamental theorem of calculus Lesson11 Integration by parts, Integration by substitution Lesson12 Integrals of rational functions Lesson13 Integrals of trigonometric funtions, irratinoal functions and exponential functions Lesson14 Definitions and properties of improper integrals Lesson15 Convergence criterion of improper integrals, Beta function and Gamma function Mid-term exam. and final exam. will be given.
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. [7] Shigetoshi Kuroda, Bibunsekibun, Kyoritsu Shuppan, 2002. [8] Ichiro Tajima, Ipushiron-Delta, Kyoritsu Shuppan, 1978. [9] Tadayuki Hara, Hideaki Matsunaga, Ipushiron-Delta Ronpou Kanzen Kouryaku, Kyoritsu Shuppan, 2011. I strongly recommend that you have some books for exercises.
PC or AV used in Class,etc.
(More Details)	Black board
Learning techniques to be incorporated
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	Midterm examination (40%), Final examination (50%), Quiz (10%).
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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