| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB120000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学Ｂ |
Subject Name
（Katakana） |
カイセキガクB |
Subject Name in
English |
Analysis B |
| Instructor |
KAMIMOTO SHINGO |
Instructor
(Katakana) |
カミモト シンゴ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
3rd-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Weds3-4,Fri1-2：SCI E209 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Lectures on Black Boards |
| Credits |
2.0 |
Class Hours/Week |
|
Language of Instruction |
J
:
Japanese |
| Course Level |
3
:
Undergraduate High-Intermediate
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Complex analysis, analytic function, holomorphic function, Cauchy-Riemann equation, Cauchy's integral theorem, maximum modulus principle |
| 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 on primary theory of modern mathematics established on classical theory.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). |
|---|
Class Objectives
/Class Outline |
Cauchy's integral theorem, which is essential in complex analysis, is explained and we learn fundamental properties of holomorphic functions derived from it. |
| Class Schedule |
lesson1 Complex numbers and complex functions
lesson2 Power series and the radius of convergence
lesson3 Analytic functions
lesson4 Identity theorem
lesson5 Complex differentiation and holomorphic functions
lesson6 Cauchy-Riemann equations
lesson7 Exponential functions and trigonometric functions
lesson8 Logarithm functions and multivalued functions
lesson9 Midterm examination
lesson10 Complex path integrals and primitive functions
lesson11 Cauchy's integral theorem
lesson12 Cauchy's integral formula
lesson13 Holomorphic functions and analytic functions
lesson14 Fundamental properties of holomorphic functions
lesson15 Maximum modulus principle |
Text/Reference
Books,etc. |
If you can read Japanese books, please check the syllabus of this course written in Japanese. Otherwise, please consult at the classroom. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Black board |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Lesson1 - Lesson4 Get familiar with analytic functions.
Lesson5 - Lesson6 Understand complex differentiation.
Lesson7 - Lesson8 Get familiar with elementary functions.
Lesson9 Review the former part of this course.
Lesson10 - Lesson12 Understand how to use Cauchy's integral theorem.
Lesson13 - Lesson15 Understand fundamental properties of holomorphic functions. |
| Requirements |
It is recommended to take the course "Exercises in Analysis B" with this course. |
| Grading Method |
Midterm examination (40%), Final examination (50%), Reports and class participation (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. |