Hiroshima University Syllabus

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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
Subject Name in
Exercises in Analysis A
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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(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 
PDFs of handouts will be distributed via Teams. 
PC or AV used in
(More Details) PDFs of handouts will be distributed via Teams. 
Learning techniques to be incorporated  
Suggestions on
Preparation and
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  
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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