HB140000 Analysis C

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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) Weds3-4,Fri5-6：Online

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, Residue theorem, Riemann sphere, Linear fractional transformation, Riemann mapping theorem, Analytic continuation, Elliptic function.

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 basics of complex analysis in Analysis B, we learn important properties of meromorphic functions.

Class Schedule lesson1 Homotopy
lesson2 Cauchy's integral theorem on a simply connected domain
lesson3 Laurent expansion
lesson4 Isolated singularities
lesson5 Residue theorem
lesson6 Argument principle
lesson7 Residue calculus
lesson8 Riemann sphere
lesson9 Linear fractional transformations
lesson10 Holomorphic automorphisms on the unit disc
lesson11 Riemann mapping theorem
lesson12 Analytic continuation
lesson13 Mittag-Leffler's theorem
lesson14 Infinite product
lesson15 Elliptic functions

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 - Lesson2     Understand Cauchy's integral theorem.
Lesson3 - Lesson7     Acquire the residue calculus.
Lesson8 - Lesson10   Understand linear fractional transformations.
Lesson11                  Understand Riemann mapping theorem.
Lesson12                  Understand analytic continuation.
Lesson13 - Lesson14  Understand global properties of meromorphic functions.
Lesson15                  Understand fundamental properties of elliptic functions.

Requirements It is recommended to take the course "Exercises in Analysis C" 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.

Academic Year	2024Year	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) Weds3-4,Fri5-6：Online
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, Residue theorem, Riemann sphere, Linear fractional transformation, Riemann mapping theorem, Analytic continuation, Elliptic function.
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 basics of complex analysis in Analysis B, we learn important properties of meromorphic functions.
Class Schedule	lesson1 Homotopy lesson2 Cauchy's integral theorem on a simply connected domain lesson3 Laurent expansion lesson4 Isolated singularities lesson5 Residue theorem lesson6 Argument principle lesson7 Residue calculus lesson8 Riemann sphere lesson9 Linear fractional transformations lesson10 Holomorphic automorphisms on the unit disc lesson11 Riemann mapping theorem lesson12 Analytic continuation lesson13 Mittag-Leffler's theorem lesson14 Infinite product lesson15 Elliptic functions
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 - Lesson2 Understand Cauchy's integral theorem. Lesson3 - Lesson7 Acquire the residue calculus. Lesson8 - Lesson10 Understand linear fractional transformations. Lesson11 Understand Riemann mapping theorem. Lesson12 Understand analytic continuation. Lesson13 - Lesson14 Understand global properties of meromorphic functions. Lesson15 Understand fundamental properties of elliptic functions.
Requirements	It is recommended to take the course "Exercises in Analysis C" 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.

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