Academic Year |
2025Year |
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 |
TAKIMOTO KAZUHIRO |
Instructor (Katakana) |
タキモト カズヒロ |
Campus |
Higashi-Hiroshima |
Semester/Term |
2nd-Year, First Semester, 2Term |
Days, Periods, and Classrooms |
(2T) Weds7-8,Fri1-2:SCI E209 |
Lesson Style |
Lecture |
Lesson Style (More Details) |
Face-to-face, Online (on-demand) |
Lectures on the blackboard |
Credits |
2.0 |
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 (2nd year) students |
Keywords |
Pointwise convergence and uniform convergence, Series of functions and power series, Multivariable function, Partial differential and total differential, Chain rule, Implicit function theorem. |
Special Subject for Teacher Education |
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Special Subject |
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Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students) | |
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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 |
This course, Analysis III, is provided for understanding the sequence of functions, the series of functions, the continuity of multivariable functions, the derivatives of multivariable functions, and so on. |
Class Schedule |
Lesson1 Pointwise convergence and uniform convergence, I (Pointwise convergence and uniform convergence) Lesson2 Pointwise convergence and uniform convergence, II (The uniform limit of any sequence of continuous functions is continuous) Lesson3 Differentation and integration of a limit function Lesson4 Series of functions Lesson5 Power series, I (Radius of convergence, Abel's lemma, Limit superior and limit inferior of a sequence) Lesson6 Power series, II (Term-by-term differentiation, Term-by-term integration, Abel's theorem) Lesson7 Mid-term examination Lesson8 Topological properties of Euclidean space Lesson9 Limits of multivariable functions and their continuity, I (Defintion and elementary properties) Lesson10 Limits of multivariable functions and their continuity, II (Intermediate value theorem, Uniform continuity) Lesson11 Partial differentiation and total differentiation Lesson12 Chain rule Lesson13 Taylor's theorem for multivariable functions Lesson14 Implicit function theorem and inverse function theorem, I (Statement and proof) Lesson15 Implicit function theorem and inverse function theorem, II (Application)
Final lesson : Final examination
The proposed plan of the course may be changed in order for the students to deepen their understanding. |
Text/Reference Books,etc. |
Textbook: [1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I & II, Uchida Rokakuho, 2007.
Study-aid books: [2] Ken-Ichi Shiraiwa, Kaisekigaku-nyumon, Gakujutsu Tosho Shuppan-sha, 1981. [3] Nobuyuki Suita and Tsunehiko Shimbo, Rikokei-no-Bibunsekibun-gaku, Gakujutsu Tosho Shuppan-sha, 1987. [4] Koji Kasahara, Bibunsekibun-gaku, Saiensu-sha, 1974. [5] Kunihiko Kodaira, Kaiseki-nyumon I, Iwanami Shoten, 2003. [6] Teiji Takagi, Kaiseki-gairon, 3rd Edition, Iwanami Shoten, 1983.
I strongly recommend that you have some books for exercises. |
PC or AV used in Class,etc. |
Handouts, Visual Materials |
(More Details) |
I will hand out some documentations if necessary. |
Learning techniques to be incorporated |
Post-class Report |
Suggestions on Preparation and Review |
Lesson 1--Lesson 15 Review is necessary. |
Requirements |
The course "Exercises in Analysis III" is given for helping and deepening your understanding. It is strongly recommended that you take this course. Please attend "Exercises in Analysis III" and solve many problems in order to understand calculus deeply. |
Grading Method |
Reports (15 percents), Midterm examination and Final examination (85 percents). If I assign some quizes, these scores are also considered. |
Practical Experience |
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Summary of Practical Experience and Class Contents based on it |
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Message |
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Other |
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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. |