| 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
English |
Exercises 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) | |
|---|
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. |
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 |
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. |