HB150000 Exercises in Analysis C

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Science

Lecture Code HB150000 Subject Classification Specialized Education

Subject Name 解析学Ｃ演習

Subject Name
（Katakana）カイセキガクCエンシュウ

Subject Name in
English Exercises in 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) Weds3-4,Fri5-6：Online

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

Blackboards and projectors are used. Sometime, prints are given. Online is also used if nesessary.

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
（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 This course is to help you understand the contents of "Analysis C." The course is given by exercise style.

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 Summary up to previous week's contents
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

Reports,quizzes, the midterm examination and the end of term examination may be given. These are proclaimed when they are given.

The plan may change according to how "Analysis B" moves on.

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. Handouts, Microsoft Teams, Microsoft Stream, moodle

(More Details) Blackboards and projectors are usually used. Copied documents are also used. In class, the instructor offers problems related to "Analysis C". Usually participants must give explanations about their answers of them using teams.

Learning techniques to be incorporated

Suggestions on
Preparation and
Review You need to make provide answers for problems offered by instructions. It is very important to prepare your answers even when you do not represent them in the class.

Requirements Participants are strongly recommended to take the course "Analysis C". This course requires contents of Analysis I - IV, Fundamental Concepts of Mathematics I and II, and also Analysis B. Participants should be familiar with how to use the knowledge on series theory including function series, and topological properties of the Euclid plane (metric, connectedness and compact subsets and so on).

Grading Method Grading is mainly based on the following factors: the results of the quizzes in every time of the lessons, the small examinations of several times, the results of the reports, the numbers of problems which you present your answer in front of all participants. In the beginning of the course, instructors will show the minimum requirements for getting the unit of this course. You should attend the first day of the course.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

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	HB150000	Subject Classification	Specialized Education
Subject Name	解析学Ｃ演習
Subject Name （Katakana）	カイセキガクCエンシュウ
Subject Name in English	Exercises in 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) Weds3-4,Fri5-6：Online
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face, Online (on-demand)
Blackboards and projectors are used. Sometime, prints are given. Online is also used if nesessary.
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 （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	This course is to help you understand the contents of "Analysis C." The course is given by exercise style.
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 Summary up to previous week's contents 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 Reports,quizzes, the midterm examination and the end of term examination may be given. These are proclaimed when they are given. The plan may change according to how "Analysis B" moves on.
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.	Handouts, Microsoft Teams, Microsoft Stream, moodle
(More Details)	Blackboards and projectors are usually used. Copied documents are also used. In class, the instructor offers problems related to "Analysis C". Usually participants must give explanations about their answers of them using teams.
Learning techniques to be incorporated
Suggestions on Preparation and Review	You need to make provide answers for problems offered by instructions. It is very important to prepare your answers even when you do not represent them in the class.
Requirements	Participants are strongly recommended to take the course "Analysis C". This course requires contents of Analysis I - IV, Fundamental Concepts of Mathematics I and II, and also Analysis B. Participants should be familiar with how to use the knowledge on series theory including function series, and topological properties of the Euclid plane (metric, connectedness and compact subsets and so on).
Grading Method	Grading is mainly based on the following factors: the results of the quizzes in every time of the lessons, the small examinations of several times, the results of the reports, the numbers of problems which you present your answer in front of all participants. In the beginning of the course, instructors will show the minimum requirements for getting the unit of this course. You should attend the first day of the course.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
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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