| Academic Year |
2026Year |
School/Graduate School |
School of Science |
| Lecture Code |
HA075000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学III演習 |
Subject Name
（Katakana） |
カイセキガク３エンシユウ |
Subject Name in
English |
Exercises in Analysis III |
| Instructor |
HIRATA KENTARO |
Instructor
(Katakana) |
ヒラタ ケンタロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
2nd-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Fri1-4：SCI E104 |
| 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 |
Pointwise and uniform convergences, power series, multivariable functions, partial differentiability, totally differentiability, chain rule |
| 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 III concerning the convergence of a sequence of functions and series of functions, as well as differentiation and its properties of multivariable functions, through exercises. |
| Class Schedule |
lesson1 Convergence of sequences of functions
lesson2 Limit functions of sequences of continuous functions
lesson3 Changing the order of limit sign and differential or integral sign
lesson4 Convergence of series of functions and Weierstrass' M-test
lesson5 Radius of convergence for power series and Abel's lemma
lesson6 Term-by-Term Differentiation and Term-by-Term Integration
lesson7 Summary of the first half
lesson8 Topological properties in Euclidean space
lesson9 Limits of multivariable functions
lesson10 Continuity of multivariable functions
lesson11 Partial differentiation and totally differentiation
lesson12 Differentiability of composition of functions(1)
lesson13 Differentiability of composition of functions(2)
lesson14 Taylor's theorem for multivariable functions(1)
lesson15 Taylor's theorem for multivariable functions(2)
Quizzes will be given without prior notice.
The above schedule is subject to change based on the progress of lecture Analysis III. |
Text/Reference
Books,etc. |
Study-aid books are the same as Analysis III. |
PC or AV used in
Class,etc. |
Handouts, Microsoft Teams, moodle |
| (More Details) |
|
| Learning techniques to be incorporated |
Discussions |
Suggestions on
Preparation and
Review |
To deepen understanding of the content in Analysis III, be sure to solve all the problems in Section A. |
| Requirements |
Take Analysis III(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. |