Hiroshima University Syllabus

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Japanese
Academic Year 2025Year School/Graduate School School of Science
Lecture Code HA065000 Subject Classification Specialized Education
Subject Name 解析学III
Subject Name
(Katakana)
カイセキガク3
Subject Name in
English
Analysis III
Instructor TAKIMOTO KAZUHIRO
Instructor
(Katakana)
タキモト カズヒロ
Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Weds7-8,Fri1-2:SCI E209
Lesson Style Lecture Lesson Style
(More Details)
Face-to-face, Online (on-demand)
Lectures on the 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 Sophomore (2nd year) students
Keywords Pointwise convergence and uniform convergence, Series of functions and power series, Multivariable function, Partial differential and total differential, Chain rule, Implicit function theorem. 
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, Analysis III, is provided for understanding the sequence of functions, the series of functions, the continuity of multivariable functions, the derivatives of multivariable functions, and so on. 
Class Schedule Lesson1 Pointwise convergence and uniform convergence, I (Pointwise convergence and uniform convergence)
Lesson2 Pointwise convergence and uniform convergence, II (The uniform limit of any sequence of continuous functions is continuous)
Lesson3 Differentation and integration of a limit function
Lesson4 Series of functions
Lesson5 Power series, I (Radius of convergence, Abel's lemma, Limit superior and limit inferior of a sequence)
Lesson6 Power series, II (Term-by-term differentiation, Term-by-term integration, Abel's theorem)
Lesson7 Mid-term examination
Lesson8 Topological properties of Euclidean space
Lesson9 Limits of multivariable functions and their continuity, I (Defintion and elementary properties)
Lesson10 Limits of multivariable functions and their continuity, II (Intermediate value theorem, Uniform continuity)
Lesson11 Partial differentiation and total differentiation
Lesson12 Chain rule
Lesson13 Taylor's theorem for multivariable functions
Lesson14 Implicit function theorem and inverse function theorem, I (Statement and proof)
Lesson15 Implicit function theorem and inverse function theorem, II (Application)

Final lesson : Final examination

The proposed plan of the course may be changed in order for the students to deepen their understanding. 
Text/Reference
Books,etc.
Textbook:
[1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I & II, 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
Class,etc.
Handouts, Visual Materials
(More Details) I will hand out some documentations if necessary. 
Learning techniques to be incorporated Post-class Report
Suggestions on
Preparation and
Review
Lesson 1--Lesson 15  Review is necessary. 
Requirements The course "Exercises in Analysis III" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis III" and solve many problems in order to understand calculus deeply. 
Grading Method Reports (15 percents), Midterm examination and Final examination (85 percents).
If I assign some quizes, these scores are also considered. 
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. 
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