| Academic Year |
2026Year |
School/Graduate School |
School of Science |
| Lecture Code |
HA095000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学IV演習 |
Subject Name
（Katakana） |
カイセキガク４エンシユウ |
Subject Name in
English |
Exercises in Analysis IV |
| Instructor |
HIRATA KENTARO |
Instructor
(Katakana) |
ヒラタ ケンタロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
2nd-Year, Second Semester, 4Term |
| Days, Periods, and Classrooms |
(4T) Tues5-6,Fri5-6：SCI E211 |
| Lesson Style |
Seminar |
Lesson Style
(More Details) |
Face-to-face |
| Presentation, exercise, discussion |
| Credits |
1.0 |
Class Hours/Week |
4 |
Language of Instruction |
J
:
Japanese |
| Course Level |
2
:
Undergraduate Low-Intermediate
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
Sophomore students in Department of Mathematics |
| Keywords |
Extremal problem for multivariable functions, Lagrange's multiplier, multiple integral, iterated integral, improper multiple integral, change of variables, surface area |
| 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 classical basic theory which is a base of modern mathematics. Being able to find and explain issues from specific events.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). |
|---|
Class Objectives
/Class Outline |
The aim of this class is to deepen understanding of the content in Analysis IV through exercises. |
| Class Schedule |
lesson1 Review of Analysis III
lesson2 Extremal problem for multivariable functions
lesson3 Criterion for local extremum
lesson4 Conditional extremal problem
lesson5 Multiple integrals over rectangles
lesson6 Integrability of functions over rectangles
lesson7 Iterated integrals
lesson8 Definition of multiple integrals on bounded sets
lesson9 Measurable sets in the sense of Jordan
lesson10 Area and volume
lesson11 Improper multiple integrals for nonnegative multivariable functions
lesson12 Improper multiple integrals for arbitrary multivariable functions
lesson13 Jacobian of diffeomorphism
lesson14 Change of variables
lesson15 Changing the order of integral and limit signs
Quizzes will be given without prior notice.
The above schedule is subject to change based on the progress of Analysis IV. |
Text/Reference
Books,etc. |
Text book is not specified, but exercise problems will be distributed. |
PC or AV used in
Class,etc. |
Handouts, Microsoft Teams, moodle |
| (More Details) |
Blackboard |
| Learning techniques to be incorporated |
Discussions |
Suggestions on
Preparation and
Review |
To deepen understanding of Analysis IV, be sure to solve all the problems in Section A. |
| Requirements |
Take Analysis IV(lecture). |
| Grading Method |
Based on quizzes (80%) and presentation (20%). |
| 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. |