| Academic Year |
2025Year |
School/Graduate School |
School of Science |
| Lecture Code |
HA020000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学I |
Subject Name
（Katakana） |
カイセキガク１ |
Subject Name in
English |
Analysis I |
| Instructor |
NAITO YUKI |
Instructor
(Katakana) |
ナイトウ ユウキ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Weds5-6,Fri5-6：SCI E104 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face, Online (on-demand) |
| Lectures are given face-to-face or online depending on the situation. |
| 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 |
Freshman (1st year) students |
| Keywords |
Continuity of real numbers, Convergence and divergence of sequences, Series, Continuity of functions, Derivative. |
| 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 I, is provided for understanding the continuity of real numbers, the limit of sequences, the continuity of functions and so on, rigorously. |
| Class Schedule |
Lesson1 Continuity of real numbers, I : Supremum, Infimum, Maximum, Minimum
Lesson2 Continuity of real numbers, II : Continuity of real numbers
Lesson3 Sequences, I : Sequences and limits
Lesson4 Sequences, II : Properties of limits
Lesson5 Sequences, III : Divergence to infinity
Lesson6 Sequences, IV : Cauchy sequences
Lesson7 Limit of functions
Lesson8 Mid-term examination
Lesson9 Limits of functions: fundamental properties
Lesson10 Limits of functions and limits of sequences
Lesson11 Properties of continuous functions
Lesson12 Series, I : Convergence, Divergence
Lesson13 Series, II : Radius of convergence
Lesson14 Series, III : Absolute convergence, Conditional convergence
Lesson15 Inverse trigonometric functions |
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, Visual Materials |
| (More Details) |
Black board |
| Learning techniques to be incorporated |
Post-class Report |
Suggestions on
Preparation and
Review |
Lesson 1--Lesson 15 Review is necessary. |
| Requirements |
The course "Exercises in Analysis I" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis I" and solve many problems in order to understand calculus deeply. |
| Grading Method |
Reports and class participation (10 %), Midterm examination (40%), 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. |