Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HA500000 Subject Classification Specialized Education
Subject Name 解析学I演習
Subject Name
Subject Name in
Exercises in Analysis I
タキモト カズヒロ,コレエダ ヨシムネ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Weds5-6,Fri5-6:SCI E209,SCI E211
Lesson Style Seminar Lesson Style
(More Details)
Exercises and presentations on the blackboard 
Credits 1.0 Class Hours/Week   Language of Instruction J : Japanese
Course Level 1 : Undergraduate Introductory
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students Freshman (1st year) students
Keywords Continuity of real numbers, Convergence and divergence of sequences, Series, Continuity of functions, Derivative. 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(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
The course, Exercises in Analysis I, is given for helping your understanding of the contents of "Analysis I". 
Class Schedule Lesson1 Continuity of real numbers, I (Supremum, Infimum, Maximum, Minimum)
Lesson2 Continuity of real numbers, II (Axiom of the continutity of real numbers)
Lesson3 Sequences, I (Defintion of the limit, convegence and divergence)
Lesson4 Sequences, II (Elementary properties)
Lesson5 Sequences, III (Cauchy sequence, Completeness of real numbers)
Lesson6 Series, I (Definition of convergence and divergence)
Lesson7 Series, II (Method of convergence criteria)
Lesson8 Series, III (Alternating series, Absolute convergence and conditional convergence)
Lesson9 Review
Lesson10 Limits of functions and continuous functions, I (Defintion and elementary properties)
Lesson11 Limits of functions and continuous functions, II (Extreme value theorem, Intermediate value theorem)
Lesson12 Limits of functions and continuous functions, III (Continuity of inverse function, Uniform continuity)
Lesson13 Derivatives, I (Defintion and elementary properties)
Lesson14 Derivatives, II (Derivative of composite function, Derivative of inverse function)
Lesson15 Derivatives, III (Mean-value theorem)

Some quizes and some reports may be assigned. 
[1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I, Uchida Rokakuho, 2007.

Study-aid books:
[2] Ken-Ichi Shiraiwa, Kaisekigaku-nyumon, Gakujutsu Tosho Shuppan-sha, 1981.
[3] Nobuyuki Suita and Tsunehiko Shimbo, Rikokei-no-Bibunsekibun-gaku, Gakujutsu Tosho Shuppan-sha, 1987.
[4] Koji Kasahara, Bibunsekibun-gaku, Saiensu-sha, 1974.
[5] Kunihiko Kodaira, Kaiseki-nyumon I, Iwanami Shoten, 2003.
[6] Teiji Takagi, Kaiseki-gairon, 3rd Edition, Iwanami Shoten, 1983.

I strongly recommend that you have some books for exercises. 
PC or AV used in
(More Details) I will hand out some documentations if necessary. 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Lesson1--Lesson15  Preparation and review are necessary. 
Requirements It is strongly recommended that you take the course "Analysis I". 
Grading Method Mark given in a class (65 percents), Midterm examination and final examinations (35 percents). 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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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