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

EnglishResearch 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 OutlineThe 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.