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 |
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Special Subject |
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Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students) | |
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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. |
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(More Details) |
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Learning techniques to be incorporated |
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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 |
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Summary of Practical Experience and Class Contents based on it |
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Message |
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Other |
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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. |