HB130000 Exercises in Analysis B

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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) Thur5-6,Fri5-6：SCI E209

Lesson Style Seminar Lesson Style
(More Details) 　

Exercise, discussion, presentation.

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 Junior (third year) students

Keywords Analytic function, identity theorem, Cauchy-Riemann equation, holomorphic function, complex integral, Cauchy's integral theorem and formula, maximum principle

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 aim is to deepen the understanding of the contents of Analysis B through the exercise and presentation.

Class Schedule lesson1 Complex numbers and functions
lesson2 Power series and radius of convergence
lesson3 Analytic functions
lesson4 Identity theorem
lesson5 Complex differentiability and holomorphic functions
lesson6 Cauchy-Riemann equation
lesson7 Complex exponential and trigonometric functions
lesson8 Review of the first half
lesson9 Complex logarithmic functions and multivalued functions
lesson10 Complex line integrals and primitive functions
lesson11 Cauchy's integral theorem
lesson12 Cauchy's integral representation
lesson13 Holomorphic function and analytic function
lesson14 Basic properties of holomorphic functions
lesson15 Maximum principle

Quizzes will be held about 3 times.

Text/Reference
Books,etc. Text: Not specified.
Study-aid book: see the syllabus of Analysis B.

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Lessons 1-15: Understand the contents of Analysis B and solve many practice problems.

Requirements

Grading Method Based on presentation (30%), quiz (60%), confirmation tests (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	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) Thur5-6,Fri5-6：SCI E209
Lesson Style	Seminar	Lesson Style (More Details)
Exercise, discussion, presentation.
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	Junior (third year) students
Keywords	Analytic function, identity theorem, Cauchy-Riemann equation, holomorphic function, complex integral, Cauchy's integral theorem and formula, maximum principle
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 aim is to deepen the understanding of the contents of Analysis B through the exercise and presentation.
Class Schedule	lesson1 Complex numbers and functions lesson2 Power series and radius of convergence lesson3 Analytic functions lesson4 Identity theorem lesson5 Complex differentiability and holomorphic functions lesson6 Cauchy-Riemann equation lesson7 Complex exponential and trigonometric functions lesson8 Review of the first half lesson9 Complex logarithmic functions and multivalued functions lesson10 Complex line integrals and primitive functions lesson11 Cauchy's integral theorem lesson12 Cauchy's integral representation lesson13 Holomorphic function and analytic function lesson14 Basic properties of holomorphic functions lesson15 Maximum principle Quizzes will be held about 3 times.
Text/Reference Books,etc.	Text: Not specified. Study-aid book: see the syllabus of Analysis B.
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lessons 1-15: Understand the contents of Analysis B and solve many practice problems.
Requirements
Grading Method	Based on presentation (30%), quiz (60%), confirmation tests (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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