Hiroshima University Syllabus

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Japanese
Academic Year 2025Year School/Graduate School School of Science
Lecture Code HB100000 Subject Classification Specialized Education
Subject Name 解析学A
Subject Name
(Katakana)
カイセキガクA
Subject Name in
English
Analysis A
Instructor To be announced.,INOUE AKIHIKO
Instructor
(Katakana)
タントウキョウインミテイ,イノウエ アキヒコ
Campus Higashi-Hiroshima Semester/Term 3rd-Year,  First Semester,  2Term
Days, Periods, and Classrooms (2T) Weds1-2,Fri3-4:Online
Lesson Style Lecture Lesson Style
(More Details)
Face-to-face
Lectures using blackboards
 
Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese
Course Level 3 : Undergraduate High-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords measure, sigma-additivity, measurable function, integration, monotone convergence theorem, dominated convergence theorem, Lebesgue measure, product measure, Fubini's 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 on primary theory of modern mathematics established on classical theory.
(Abilities and Skills)
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). 
Class Objectives
/Class Outline
"Measure" is an abstraction of the concept of "quantity" such as length, area, volume, mass, probability, and number. Measure theory and the theory of integration based on it are extremely useful in various mathematical fields such as analysis, probability theory, and statistics, as well as in their applications. In this lecture, we will learn about measure theory and the theory of integration. 
Class Schedule Simple Functions, Measurable Functions, Construction of integrals and their basic properties, Monotone Convergence Theorem, Fatou's Lemma, Dominated Convergence Theorem, Sets of Measure 0, Product measure, Fubini's Theorem
 
Text/Reference
Books,etc.
To be instructed by the teacher. 
PC or AV used in
Class,etc.
(More Details)  
Learning techniques to be incorporated
Suggestions on
Preparation and
Review
Try to draw figures as much as possible so that you can intuitively understand the discussions.  
Requirements Students are supposed to attend Exercises in Analysis A as well 
Grading Method To be announced by the teacher.
 
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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