Hiroshima University Syllabus |

Japanese

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

（Katakana）カイセキガクニエンシュウ Subject Name in

EnglishExercises in Analysis ＩＩ Instructor HIRATA KENTARO,CASTELLANOS LUIS PEDRO Instructor

(Katakana)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

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 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.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

ReviewLesson 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 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.