CC221404 Introduction to Analysis II

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Education

Lecture Code CC221404 Subject Classification Specialized Education

Subject Name 解析学概論II

Subject Name
（Katakana）カイセキガクガイロンII

Subject Name in
English Introduction to Analysis II

Instructor IKEHATA RYO

Instructor
(Katakana) イケハタ　リョウ

Campus Higashi-Hiroshima Semester/Term 2nd-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Weds5-8：EDU L204

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Lecture by using blackboard

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-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 To study the fundamental knowldge of the differential and integral calculus.

Class Schedule lesson1:Orientation & introductory test
lesson2:Review of the mean value theorem ①
lesson3:Review of the mean value theorem ② and related topics
lesson4:Convergence of point sequences　
lesson5:On the completeness of two-dimensional space
lesson6:On the closed and open sets ①
lesson7:On the closed and open sets ②
lesson8:Definition and properties of continuous functions in two-dimensional space
lesson9:Definition and Properties of Partial Differentiation ①
lesson10:Definition and Properties of Partial Differentiation ②
lesson11:On the differentiability of two-variable functions
lesson12:On the differentiability and its properties of two-variable functions
lesson13:On Taylor Expansion of Two-Variable Functions
lesson14:On the local maxima and local minima of two-variable functions ①
lesson15:On the local maxima and local minima of two-variable functions ②

Several reports and final exam

It is recommended that students have already taken calculus for one variable.

Text/Reference
Books,etc. I will introduce several texts at the first lesson.

PC or AV used in
Class,etc.

(More Details) None

Learning techniques to be incorporated Discussions

Suggestions on
Preparation and
Review Students must prestudy necessarily. Since the so-called ε-N logic is used frequently, it is a prerequisite that you have already learned about it.

Requirements

Grading Method To be determined by the results of several report assignments and final examination.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Lecture notes recorded during the lecture may be brought to the examination.

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	2025Year	School/Graduate School	School of Education
Lecture Code	CC221404	Subject Classification	Specialized Education
Subject Name	解析学概論II
Subject Name （Katakana）	カイセキガクガイロンII
Subject Name in English	Introduction to Analysis II
Instructor	IKEHATA RYO
Instructor (Katakana)	イケハタ　リョウ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Weds5-8：EDU L204
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Lecture by using blackboard
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-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	To study the fundamental knowldge of the differential and integral calculus.
Class Schedule	lesson1:Orientation & introductory test lesson2:Review of the mean value theorem ① lesson3:Review of the mean value theorem ② and related topics lesson4:Convergence of point sequences　 lesson5:On the completeness of two-dimensional space lesson6:On the closed and open sets ① lesson7:On the closed and open sets ② lesson8:Definition and properties of continuous functions in two-dimensional space lesson9:Definition and Properties of Partial Differentiation ① lesson10:Definition and Properties of Partial Differentiation ② lesson11:On the differentiability of two-variable functions lesson12:On the differentiability and its properties of two-variable functions lesson13:On Taylor Expansion of Two-Variable Functions lesson14:On the local maxima and local minima of two-variable functions ① lesson15:On the local maxima and local minima of two-variable functions ② Several reports and final exam It is recommended that students have already taken calculus for one variable.
Text/Reference Books,etc.	I will introduce several texts at the first lesson.
PC or AV used in Class,etc.
(More Details)	None
Learning techniques to be incorporated	Discussions
Suggestions on Preparation and Review	Students must prestudy necessarily. Since the so-called ε-N logic is used frequently, it is a prerequisite that you have already learned about it.
Requirements
Grading Method	To be determined by the results of several report assignments and final examination.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Lecture notes recorded during the lecture may be brought to the examination.
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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