| Academic Year |
2025Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB130000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学Ｂ演習 |
Subject Name
（Katakana） |
カイセキガクBエンシュウ |
Subject Name in
English |
Exercises in Analysis B |
| Instructor |
HIRATA KENTARO |
Instructor
(Katakana) |
ヒラタ ケンタロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
3rd-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Fri1-4：SCI E209 |
| Lesson Style |
Seminar |
Lesson Style
(More Details) |
Face-to-face |
| |
| Credits |
2.0 |
Class Hours/Week |
4 |
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 |
Third year Mathematics Students |
| Keywords |
Complex number, holomorphic function, Cauchy-Riemann equation, complex integral, Cauchy integral theorem and formula, Taylor expansion, Identity theorem, etc. |
| 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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions. |
|---|
Class Objectives
/Class Outline |
The purpose of this class is to deepen understanding on the contents of Analysis B including several complex functions, complex differentiability, equivalent conditions for analyticity, several properties of holomorphic functions, etc. |
| Class Schedule |
lesson1 Complex number and polar representation
lesson2 Complex sequence and series
lesson3 Absolute convergent series and convergence tests
lesson4 Power series and radius of convergence
lesson5 complex differentiability and holomorphic function
lesson6 Cauchy-Riemann equation and complex exponential
lesson7 Complex trigonometric and logarithmic functions
lesson8 Complex power function and complex line integral
lesson9 midterm examination
lesson10 Calculation of complex line integrals
lesson11 Function series and existence condition for primitive function
lesson12 Cauchy's integral theorem
lesson13 Cauchy's integral formula and Taylor expansion
lesson14 Zeros and identity theorem
lesson15 Properties of holomorphic functions, Summary
The common midterm examination for both lecture and exercise will be held on May 9. Also, the common final examination will be held on June 3 or 4. |
Text/Reference
Books,etc. |
[Text book] Not specified.
[Study-aid books]
There are many (Japanese) books on complex analysis or holomorphic functions. I recommend that you use books that best suit your needs. |
PC or AV used in
Class,etc. |
Handouts, Visual Materials, Microsoft Teams, moodle |
| (More Details) |
|
| Learning techniques to be incorporated |
Discussions |
Suggestions on
Preparation and
Review |
For every lesson: It is advisable to organize your notes to check the parts you do not fully understand, and to deepen your understanding by reading the relevant parts of study-aid books and solving exercises. |
| Requirements |
It is assumed that students understand Analysis I--IV and also take the Analysis B class. |
| Grading Method |
Based on midterm exam (40%), final exam (40%) and presentation (and quizzes) (20%). |
| 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. |