| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HA065000 |
Subject Classification |
Specialized Education |
| Subject Name |
解析学III |
Subject Name
（Katakana） |
カイセキガク３ |
Subject Name in
English |
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) Tues3-4,Fri1-2：SCI E209 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| |
| Credits |
2.0 |
Class Hours/Week |
|
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 in the department of Mathematics |
| Keywords |
Sequence of functions, series of functions, power series, uniform convergence, radius of convergence, functions of several variables, partial differentiability, total differentiability, Taylor'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 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 the first half is to understand uniform convergence of sequences and series of functions as well as related theorems. The second half is devoted to partial differentiability, totally differentiability and related theorems for functions of several variables. |
| Class Schedule |
lesson1 Uniform convergence of sequences of functions
lesson2 Theorems on uniform convergent sequences of continuous functions
lesson3 Series of functions and M-test
lesson4 Power series and radius of convergence
lesson5 Invariance of radius of convergence and range where a power series converges
lesson6 Supplement regarding L1 to L5
lesson7 Topological properties in the Euclidean space
lesson8 Limits and continuity of functions of several variables
lesson9 Midterm exam.
lesson10 Partial differentiability
lesson11 Total differentiability
lesson12 Partial differentiability of composite functions
lesson13 Taylor's theorem
lesson14 Extremal problem
lesson15 Implicit function theorem
Midterm exam and term-end exam.
The above information may be changed depending on the progress of the class, or the content of the class may be changed depending on the situation. |
Text/Reference
Books,etc. |
Textbook: Not assigned, but distribute handouts. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Blackboard |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Be sure to review after each lesson. |
| Requirements |
The lecture will be given assuming the students have taken the Analysis III-exercise class. |
| Grading Method |
Midterm exam (40%), Term-end exam (50%), Quiz (10%) |
| 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. |