| Academic Year |
2024Year |
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 |
INOUE AKIHIKO |
Instructor
(Katakana) |
イノウエ アキヒコ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
3rd-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Tues7-8,Thur1-2：SCI E210 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
Lectures by Teams and ipad. Face-to-face examination.
|
| Credits |
2.0 |
Class Hours/Week |
|
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 |
lesson1 Lebesgue's idea
lesson2 Integration of simple functions
lesson3 Integration of measurable functions
lesson4 Monotone convergence theorem
lesson5 Dominated convergence theorem
lesson6 Sets of measure 0
lesson7 1-dimensional integration and primitive function
lesson8 1-dimensional integration by parts and change of variable
lesson9 1-dimensional integration -- explicit examples
lesson10 Existence of 1-dimensional Lebesgue measure
lesson11 Uniqueness of extension and its application
lesson12 2-dimensional Lebesgue measure
lesson13 Dynkin class theorem
lesson14 Fubini's theorem and application
lesson15 Fubini's theorem and application--continued |
Text/Reference
Books,etc. |
The PDF of the notes will be distributed through Teams. |
PC or AV used in
Class,etc. |
|
| (More Details) |
The PDF of the notes |
| 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. Also, when reviewing, it is effective to reproduce the discussions you have learned in your notes without looking at anything. |
| Requirements |
Students are supposed to attend Exercises in Analysis A as well |
| Grading Method |
Term paper 25%, Examination 75%.
|
| 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. |