CC223005 Research Methods in Analysis I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Education

Lecture Code CC223005 Subject Classification Specialized Education

Subject Name 解析学研究法I

Subject Name
（Katakana）カイセキガクケンキュウホウI

Subject Name in
English Research Methods in Analysis I

Instructor SHIMOMURA TETSU

Instructor
(Katakana) シモムラ　テツ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, First Semester, 2Term

Days, Periods, and Classrooms (2T) Weds1-4：EDU L206

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture- and Exercise-oriented, Note-taking, Discussions, Student presentations, Field work, Work. Chemicals will be used.

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

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) Secondary School Mathematics Education
（Knowledge and Understanding）
・To understand basic knowledge of teaching contents of mathematic education.
（Abilities and Skills）
・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.

Class Objectives
/Class Outline The objective of this course is for students to learn the fundamentals of functions with complex numbers as variables based on the foundation of calculus and complex numbers that you learned in high school mathematics and the first year of the university. Students will also deepen understanding of the contents of analysis in school mathematics.

Class Schedule lesson1
lesson2
lesson3
lesson4
lesson5
lesson6
lesson7
lesson8
lesson9
lesson10
lesson11
lesson12
lesson13
lesson14
lesson15

"
Lesson1: Course Outline
Student will be provided with an overview of this course to clarify the objective and raise their awareness of the issues.
Lesson2: Complex Numbers and Complex Plane
　Make necessary preparations regarding complex numbers and complex plane
Lesson3: Functions of Complex Variables
The instructor will explain limit values and continuity of functions of complex variables
Lesson4: Holomorphic Functions
The instructor will define holomorphic functions and explain necessary and sufficient conditions for holomorphic functions of complex variables.
Lesson5: Elementary Functions
The instructor will define elementary functions, which are important complex variables and explain their properties.
Lesson6: Supplementation of the learning contents and Exercises.
Supplement the learning contents from Lesson2-5 and do exercises.
Lesson7: Complex Integral
The instructor will define complex integrals and explain the basic properties of complex integrals
Lesson8: Cauchy Integral Theorem
The instructor will explain the Cauchy’s integral theorem.
Lesson9: Series Expansion (1)
The instructor will explain expansion into power series of holomorphic functions.
Lesson10: Basic Properties of Holomorphic Functions
The instructor will explain the principles of maximum modulus.
Lesson11: Supplementation of the learning contents and Exercises.
Supplement the learning contents from Lesson7-10 and do exercises.
Lesson12: Series Expansion (2)
The instructor will explain series expansion of holomorphic functions in an annular region。
Lesson13: Residue
The instructor will explain residue and residue theorem.
Lesson14: Calculation of Definite Integrals
This lesson is to show that a value for a definite integral of a real variable function and a value of an infinite integral can be found by using Cauchy integral theorem and residue theorem.
Lesson15: Supplementation of the learning contents, Exercises, and Final Exam
Supplement the learning contents of the previous lessons and do exercises. There will be a final exam.
"

Text/Reference
Books,etc. "Lecture Style(Lecture-oriented;Note-taking)
複素解析　矢野健太郎　石原繁著　裳華房。
複素関数論　岸正倫　藤本垣孝著　学術図書出版社。
複素数３０講　志賀浩二　朝倉書店。
キーポイント複素関数　表実　岩波書店。
"

PC or AV used in
Class,etc. 　

(More Details) Textbooks, Handouts, Audio materials, Movies( Video/PC/other image materials)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review "After Lesson1:
　Review the contents of the lesson.
After Lesson2 -5:
　Review the contents of the lesson.
After Lesson6:
Review the contents of Lesson 1-6.
After Lesson7-10:
　Review the contents of the lesson.
After Lesson11:
　Review the contents of Lesson 7-11.
After Lesson12-14
　Review the contents of the lessons.
After Lesson15:
　Review the contents of all of the lessons."

Requirements

Grading Method Students will be evaluated comprehensively based on report assignment, quizzes, contribution, attendance, final exam and others. If students are absent for more than 1/3 of the course, they will not be allowed to take a final exam. Students' ' Knowledge & Understanding 3' and ' Intellectual capabilities and skills 3' will be evaluated based mainly on final exam and quizzes.

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 Education
Lecture Code	CC223005	Subject Classification	Specialized Education
Subject Name	解析学研究法I
Subject Name （Katakana）	カイセキガクケンキュウホウI
Subject Name in English	Research Methods in Analysis I
Instructor	SHIMOMURA TETSU
Instructor (Katakana)	シモムラ　テツ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Weds1-4：EDU L206
Lesson Style	Lecture	Lesson Style (More Details)
Lecture- and Exercise-oriented, Note-taking, Discussions, Student presentations, Field work, Work. Chemicals will be used.
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
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)	Secondary School Mathematics Education （Knowledge and Understanding）・To understand basic knowledge of teaching contents of mathematic education. （Abilities and Skills）・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.
Class Objectives /Class Outline	The objective of this course is for students to learn the fundamentals of functions with complex numbers as variables based on the foundation of calculus and complex numbers that you learned in high school mathematics and the first year of the university. Students will also deepen understanding of the contents of analysis in school mathematics.
Class Schedule	lesson1 lesson2 lesson3 lesson4 lesson5 lesson6 lesson7 lesson8 lesson9 lesson10 lesson11 lesson12 lesson13 lesson14 lesson15 " Lesson1: Course Outline Student will be provided with an overview of this course to clarify the objective and raise their awareness of the issues. Lesson2: Complex Numbers and Complex Plane 　Make necessary preparations regarding complex numbers and complex plane Lesson3: Functions of Complex Variables The instructor will explain limit values and continuity of functions of complex variables Lesson4: Holomorphic Functions The instructor will define holomorphic functions and explain necessary and sufficient conditions for holomorphic functions of complex variables. Lesson5: Elementary Functions The instructor will define elementary functions, which are important complex variables and explain their properties. Lesson6: Supplementation of the learning contents and Exercises. Supplement the learning contents from Lesson2-5 and do exercises. Lesson7: Complex Integral The instructor will define complex integrals and explain the basic properties of complex integrals Lesson8: Cauchy Integral Theorem The instructor will explain the Cauchy’s integral theorem. Lesson9: Series Expansion (1) The instructor will explain expansion into power series of holomorphic functions. Lesson10: Basic Properties of Holomorphic Functions The instructor will explain the principles of maximum modulus. Lesson11: Supplementation of the learning contents and Exercises. Supplement the learning contents from Lesson7-10 and do exercises. Lesson12: Series Expansion (2) The instructor will explain series expansion of holomorphic functions in an annular region。 Lesson13: Residue The instructor will explain residue and residue theorem. Lesson14: Calculation of Definite Integrals This lesson is to show that a value for a definite integral of a real variable function and a value of an infinite integral can be found by using Cauchy integral theorem and residue theorem. Lesson15: Supplementation of the learning contents, Exercises, and Final Exam Supplement the learning contents of the previous lessons and do exercises. There will be a final exam. "
Text/Reference Books,etc.	"Lecture Style(Lecture-oriented;Note-taking) 複素解析　矢野健太郎　石原繁著　裳華房。複素関数論　岸正倫　藤本垣孝著　学術図書出版社。複素数３０講　志賀浩二　朝倉書店。キーポイント複素関数　表実　岩波書店。 "
PC or AV used in Class,etc.
(More Details)	Textbooks, Handouts, Audio materials, Movies( Video/PC/other image materials)
Learning techniques to be incorporated
Suggestions on Preparation and Review	"After Lesson1: 　Review the contents of the lesson. After Lesson2 -5: 　Review the contents of the lesson. After Lesson6: Review the contents of Lesson 1-6. After Lesson7-10: 　Review the contents of the lesson. After Lesson11: 　Review the contents of Lesson 7-11. After Lesson12-14 　Review the contents of the lessons. After Lesson15: 　Review the contents of all of the lessons."
Requirements
Grading Method	Students will be evaluated comprehensively based on report assignment, quizzes, contribution, attendance, final exam and others. If students are absent for more than 1/3 of the course, they will not be allowed to take a final exam. Students' ' Knowledge & Understanding 3' and ' Intellectual capabilities and skills 3' will be evaluated based mainly on final exam and quizzes.
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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