Hiroshima University Syllabus

Back to syllabus main page
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. 
Back to syllabus main page