HB140000 Analysis C

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Science

Lecture Code HB140000 Subject Classification Specialized Education

Subject Name 解析学Ｃ

Subject Name
（Katakana）カイセキガクC

Subject Name in
English Analysis C

Instructor KAWASHITA MISHIO

Instructor
(Katakana) カワシタ　ミシオ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, Second Semester, 3Term

Days, Periods, and Classrooms (3T) Tues7-8,Thur5-6：Online

Lesson Style Lecture Lesson Style
(More Details) Face-to-face, Online (on-demand)

Blackboards and projectors are used. Sometime, prints are given. Basically, face-to-face style are used.

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 Junior students of department of mathematics in faculty of science

Keywords

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 Based on the basic theory of complex analysis learned in Analysis B, we will introduce some of the subsequent developments.

Class Schedule lesson1 Basic properties of holomorphic functions (review)
lesson2 Homotopy of curves
lesson3 Cauchy's integral theorem on simply connected domains
lesson4 Calculation of integrals
lesson5 Classification of isolated singularities
lesson6 Laurent expansion
lesson7 Residual theorem and argument principle
lesson8 Midterm exam.
lesson9 Riemann sphere and Riemann surfaces
lesson10 linear fractional transformations
lesson11 Mean value theorem for harmonic functions (almost review)
lesson12 Dirichlet boundary value problem for Laplacian
lesson13 Harmonic functions on the unit disc and Poisson kernel
lesson14 Fourier series expansion for periodic functions
lesson15 Heat equation and Fourier series expansion

Midterm and final exams will be held. The midterm exam is scheduled for the 8th lesson, but this may change depending on circumstances. The final exam will be held during the final exam period.

The progress, order and content of the lessons may change depending on circumstances.

Text/Reference
Books,etc. Textbooks are not fixed. Any book entitled "Complex Analysis" is good for your textbook if you are interested in it.

PC or AV used in
Class,etc. Text, Microsoft Teams, moodle

(More Details) Blackboards and projectors are usually used. Copied documents are also used.

Learning techniques to be incorporated

Suggestions on
Preparation and
Review You need to make preparations and revisions for each lessons. Particularly, reviewing process after the lessons is important. I hope that you catch this truth from these two year's experience. To understand the contents of the lessons, you need to consider what you have to do, of what you take care, what you should do after the lessons. This is common remarks for all lessons through the first to the last.

Requirements The course "Exercises in Analysis C" is given for helping and deepening your understanding. It is strongly recommend that you take the course.

Grading Method Grading is mainly based on the results of the midterm and the end of term examinations. The imposed quizzes in the classes and the reports as homework are also into consideration for estimation of the grade.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message If your score of the midterm exam., do not give up and continue studying the contents of the course. You also keep in mind studying hard even if you get good results for the exam..

Other In Japanese universities it is not customary to bring food or drinks into the classroom unless the instructor gives permission to do so. No Drinking and No Eating in the Classroom, Please!

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.

Academic Year	2025Year	School/Graduate School	School of Science
Lecture Code	HB140000	Subject Classification	Specialized Education
Subject Name	解析学Ｃ
Subject Name （Katakana）	カイセキガクC
Subject Name in English	Analysis C
Instructor	KAWASHITA MISHIO
Instructor (Katakana)	カワシタ　ミシオ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Tues7-8,Thur5-6：Online
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face, Online (on-demand)
Blackboards and projectors are used. Sometime, prints are given. Basically, face-to-face style are used.
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	Junior students of department of mathematics in faculty of science
Keywords
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	Based on the basic theory of complex analysis learned in Analysis B, we will introduce some of the subsequent developments.
Class Schedule	lesson1 Basic properties of holomorphic functions (review) lesson2 Homotopy of curves lesson3 Cauchy's integral theorem on simply connected domains lesson4 Calculation of integrals lesson5 Classification of isolated singularities lesson6 Laurent expansion lesson7 Residual theorem and argument principle lesson8 Midterm exam. lesson9 Riemann sphere and Riemann surfaces lesson10 linear fractional transformations lesson11 Mean value theorem for harmonic functions (almost review) lesson12 Dirichlet boundary value problem for Laplacian lesson13 Harmonic functions on the unit disc and Poisson kernel lesson14 Fourier series expansion for periodic functions lesson15 Heat equation and Fourier series expansion Midterm and final exams will be held. The midterm exam is scheduled for the 8th lesson, but this may change depending on circumstances. The final exam will be held during the final exam period. The progress, order and content of the lessons may change depending on circumstances.
Text/Reference Books,etc.	Textbooks are not fixed. Any book entitled "Complex Analysis" is good for your textbook if you are interested in it.
PC or AV used in Class,etc.	Text, Microsoft Teams, moodle
(More Details)	Blackboards and projectors are usually used. Copied documents are also used.
Learning techniques to be incorporated
Suggestions on Preparation and Review	You need to make preparations and revisions for each lessons. Particularly, reviewing process after the lessons is important. I hope that you catch this truth from these two year's experience. To understand the contents of the lessons, you need to consider what you have to do, of what you take care, what you should do after the lessons. This is common remarks for all lessons through the first to the last.
Requirements	The course "Exercises in Analysis C" is given for helping and deepening your understanding. It is strongly recommend that you take the course.
Grading Method	Grading is mainly based on the results of the midterm and the end of term examinations. The imposed quizzes in the classes and the reports as homework are also into consideration for estimation of the grade.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	If your score of the midterm exam., do not give up and continue studying the contents of the course. You also keep in mind studying hard even if you get good results for the exam..
Other	In Japanese universities it is not customary to bring food or drinks into the classroom unless the instructor gives permission to do so. No Drinking and No Eating in the Classroom, Please!
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.

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