HA075000 Exercises in Analysis III

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HA075000 Subject Classification Specialized Education

Subject Name 解析学III演習

Subject Name
（Katakana）カイセキガク３エンシユウ

Subject Name in
English Exercises in Analysis III

Instructor KAWASHITA MISHIO

Instructor
(Katakana) カワシタ　ミシオ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon3-4,Weds9-10：Online

Lesson Style Seminar Lesson Style
(More Details) 　

Main perpose of this course is exercise of mathematical problems. participants should explain your answers using blackboards. The problems are given by prints.  Quizzes are held several times.

Credits 1.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Sophomore students of department of mathematics in faculty of science

Keywords Area, length of curves, series with positive terms, absolutely covergence, conditional convergence, series of functions, pointwise convergence, uniformly convergence, power series, functions with  several variables, derivatives w.r.t some direction, metric, open set, closed set, interior point, exterior point, boundary point, partial derivarive, total derivative, chain rule, Taylor expansion.

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 classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline This course is for helping your understanding the contents of "Analysis III". The course is given by exercise style.

Class Schedule lesson1 Uniform convergence of sequences of functions
lesson2 Theorems on uniform convergent sequences of continuous functions
lesson3 Series of functions and M-test
lesson4 Power series and radius of convergence
lesson5 Invariance of radius of convergence and range where a power series converges
lesson6 Supplement regarding L1 to L5
lesson7 Topological properties in the Euclidean space
lesson8 Limits and continuity of functions of several variables
lesson9 Review of previous years (corresponds to mid-term exam in class)
lesson10 Partial differentiability
lesson11 Total differentiability
lesson12 Partial differentiability of composite functions
lesson13 Taylor's theorem
lesson14 Extremal problem
lesson15 Implicit function theorem

The plan may change according to how "Analysis III" moves on. Reports and quizzes may be given.

The proposed plan of the course may change when it is better for participants understandings. Please accept changes times when lecture and exercise are done if the instructors have to do that.

Text/Reference
Books,etc. The texts are not fixed. There are many books for exercises of calculus. The instructors recommend that you keep some of them in which you are interested.

PC or AV used in
Class,etc. 　

(More Details) Blackboards are usually used. Copied documents are also used.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review You need to make preparations and revisions for each lessons.  I hope that you catch this truth from the last year's experience. For your advantages, you need to consider how do you prepair and review the contents of the courses. You should participate in the exercises after doing such preparations. This is common remarks for all lessons through the first to the last.

Requirements Participants are strongly recommended to take the course "Analysis III". The contents learned in the courses "Analysis I and exersize of it", "Analysis II and exersize of it", "Linear algebra I and exercise of it", "Linear algebra II and exercise of it" (for mathematics students), and "Introduction to Mathematics", are assumed as prerequested knowledge.

Grading Method Grading is mainly based on the results of the midterm and the end of term examinations. Grading is mainly based on the following factors: the results of the quizzes in the lessons, the results of the reports, the numbers of problems which you present your answer in front of all participants. When the midterm and final examinations are imposed, these results are also used for the final decision of the grading.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message 1. Please refrain from talking in class! If you want to speak, you should demonstrate problems which other participants can not solve. This is the task of students.
2. You may have already found that nothing had happened even if you had given wrong answers. Instead of that, you may say that now you understand well by giving bad answers in the past. In this year, almost all participants will be adults in legal sense. Then, wrong and bad behaviours are not allowed legally.  But, in studying mathematics, we can make mistakes. Nobody accuse you (but, sometimes you feel that instructors hard on you). Only errors of your answer are pointed out. Finding errors makes chances for well understanding. You need to be positive thinking like "Yes, I will understand more deeply!". In this semester, please make also many wrong answers, and find what is truth.

Other In Japanese universities it is not customary to bring food or drinks into the classroom unless the instructor gives permission to do so. No Drinking and No Eating in the Classroom, Please!

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	HA075000	Subject Classification	Specialized Education
Subject Name	解析学III演習
Subject Name （Katakana）	カイセキガク３エンシユウ
Subject Name in English	Exercises in Analysis III
Instructor	KAWASHITA MISHIO
Instructor (Katakana)	カワシタ　ミシオ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon3-4,Weds9-10：Online
Lesson Style	Seminar	Lesson Style (More Details)
Main perpose of this course is exercise of mathematical problems. participants should explain your answers using blackboards. The problems are given by prints. Quizzes are held several times.
Credits	1.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Sophomore students of department of mathematics in faculty of science
Keywords	Area, length of curves, series with positive terms, absolutely covergence, conditional convergence, series of functions, pointwise convergence, uniformly convergence, power series, functions with several variables, derivatives w.r.t some direction, metric, open set, closed set, interior point, exterior point, boundary point, partial derivarive, total derivative, chain rule, Taylor expansion.
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 classical basic theory which is a base of modern mathematics. Being able to find and explain issues from specific events. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	This course is for helping your understanding the contents of "Analysis III". The course is given by exercise style.
Class Schedule	lesson1 Uniform convergence of sequences of functions lesson2 Theorems on uniform convergent sequences of continuous functions lesson3 Series of functions and M-test lesson4 Power series and radius of convergence lesson5 Invariance of radius of convergence and range where a power series converges lesson6 Supplement regarding L1 to L5 lesson7 Topological properties in the Euclidean space lesson8 Limits and continuity of functions of several variables lesson9 Review of previous years (corresponds to mid-term exam in class) lesson10 Partial differentiability lesson11 Total differentiability lesson12 Partial differentiability of composite functions lesson13 Taylor's theorem lesson14 Extremal problem lesson15 Implicit function theorem The plan may change according to how "Analysis III" moves on. Reports and quizzes may be given. The proposed plan of the course may change when it is better for participants understandings. Please accept changes times when lecture and exercise are done if the instructors have to do that.
Text/Reference Books,etc.	The texts are not fixed. There are many books for exercises of calculus. The instructors recommend that you keep some of them in which you are interested.
PC or AV used in Class,etc.
(More Details)	Blackboards are usually used. Copied documents are also used.
Learning techniques to be incorporated
Suggestions on Preparation and Review	You need to make preparations and revisions for each lessons. I hope that you catch this truth from the last year's experience. For your advantages, you need to consider how do you prepair and review the contents of the courses. You should participate in the exercises after doing such preparations. This is common remarks for all lessons through the first to the last.
Requirements	Participants are strongly recommended to take the course "Analysis III". The contents learned in the courses "Analysis I and exersize of it", "Analysis II and exersize of it", "Linear algebra I and exercise of it", "Linear algebra II and exercise of it" (for mathematics students), and "Introduction to Mathematics", are assumed as prerequested knowledge.
Grading Method	Grading is mainly based on the results of the midterm and the end of term examinations. Grading is mainly based on the following factors: the results of the quizzes in the lessons, the results of the reports, the numbers of problems which you present your answer in front of all participants. When the midterm and final examinations are imposed, these results are also used for the final decision of the grading.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	1. Please refrain from talking in class! If you want to speak, you should demonstrate problems which other participants can not solve. This is the task of students. 2. You may have already found that nothing had happened even if you had given wrong answers. Instead of that, you may say that now you understand well by giving bad answers in the past. In this year, almost all participants will be adults in legal sense. Then, wrong and bad behaviours are not allowed legally. But, in studying mathematics, we can make mistakes. Nobody accuse you (but, sometimes you feel that instructors hard on you). Only errors of your answer are pointed out. Finding errors makes chances for well understanding. You need to be positive thinking like "Yes, I will understand more deeply!". In this semester, please make also many wrong answers, and find what is truth.
Other	In Japanese universities it is not customary to bring food or drinks into the classroom unless the instructor gives permission to do so. No Drinking and No Eating in the Classroom, Please!
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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