Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HA510000 Subject Classification Specialized Education
Subject Name 解析学II演習
Subject Name
Subject Name in
Exercises in Analysis II
ヒラタ ケンタロウ,カステヤノス モスコソ ルイス ペドロ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  4Term
Days, Periods, and Classrooms (4T) Mon3-4,Weds1-2:SCI E209
Lesson Style Seminar Lesson Style
(More Details)
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 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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(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
The course, Exercises in Analysis II, is given for helping your understanding of the contents of "Analysis II". 
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

A final exam. will be given. 
[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
(More Details) Black board 
Learning techniques to be incorporated  
Suggestions on
Preparation and
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 Quiz (30%), Presentation (20%), Final examination (50%). 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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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