| Academic Year |
2025Year |
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) Mon3-4,Tues9-10：SCI E209 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| |
| 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 |
1st year Mathematics students |
| Keywords |
Continuity, Uniform continuity, Differentiability, Taylor's theorem and expansion, Riemann integral, Primitive function, Calculation of integrals, 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 |
This course, Analysis II, is provided for understanding properties of continuous functions, properties of differentiable functions and properties of Riemann integrals, etc. |
| Class Schedule |
Lesson1 Properties of continuous functions
Lesson2 Properties of continuous functions
Lesson3 Uniform continuity
Lesson4 Differentiability
Lesson5 Differentiability of composition and inverse functions, Leibniz formula
Lesson6 Mean value theorem, l'Hospital theorem
Lesson7 Taylor's theorem
Lesson8 Taylor's expansion
Lesson9 Mid-term examination
Lesson10 Definition of Riemann integral
Lesson11 Equivalent condition for integrability, and integrability of continuous functions
Lesson12 Riemann sum, properties of integrals of continuous functions
Lesson13 Integrals of rational functions, trigonometric funtions and irratinoal functions
Lesson14 Improper integrals over finite intervals
Lesson15 Improper integrals over infinite intervals
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. |
Text, Other (see [More Details]), moodle |
| (More Details) |
Black board |
| Learning techniques to be incorporated |
Quizzes/ Quiz format |
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. |