| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB110000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学Ａ演習 |
Subject Name
（Katakana） |
カイセキガクAエンシュウ |
Subject Name in
English |
Exercises in 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) Tues9-10,Thur3-4：Online |
| Lesson Style |
Seminar |
Lesson Style
(More Details) |
|
| Simultaneous interactive online classes using Teams and iPad. Classes are recorded by Teams. Problems are assigned to you. You upload your answers to Teams. While the instructor shares your answer on the screen, you present your answer in a dialog with the instructor. Typically, some problems are assigned each time. You submit your answers using the Assign feature in Teams. |
| 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 |
Mathmatics 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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions. |
|---|
Class Objectives
/Class Outline |
You will deepen your understanding of what you have learned in Analysis A by solving problems given by your instructor and by submitting answers to assigned assignments. |
| 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. |
PDFs of handouts will be distributed via Teams. |
PC or AV used in
Class,etc. |
|
| (More Details) |
PDFs of handouts will be distributed via Teams. |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
To understand math, it is important to first try to solve problems yourself. If you don't understand a problem right away, wait a while and try again.
|
| Requirements |
Students are supposed to attend Analysis A as well |
| Grading Method |
Presentation (25%) and assignments (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. |