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

EnglishExercises 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：SCI E104 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 OutlineThis 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

ReviewYou 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.