Academic Year |
2024Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
Lecture Code |
WSA42000 |
Subject Classification |
Specialized Education |
Subject Name |
数理解析基礎講義B |
Subject Name (Katakana) |
スウリカイセキキソコウギビー |
Subject Name in English |
Mathematical Analysis B |
Instructor |
KAMIMOTO SHINGO,HIRATA KENTARO,TAKIMOTO KAZUHIRO,KAWASHITA MISHIO |
Instructor (Katakana) |
カミモト シンゴ,ヒラタ ケンタロウ,タキモト カズヒロ,カワシタ ミシオ |
Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 2Term |
Days, Periods, and Classrooms |
(2T) Mon7-8,Weds3-4:SCI E211 |
Lesson Style |
Lecture |
Lesson Style (More Details) |
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Lectures are given face-to-face or online depending on the situation. |
Credits |
2.0 |
Class Hours/Week |
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Language of Instruction |
B
:
Japanese/English |
Course Level |
5
:
Graduate Basic
|
Course Area(Area) |
25
:
Science and Technology |
Course Area(Discipline) |
01
:
Mathematics/Statistics |
Eligible Students |
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Keywords |
Holomorphic functions of several variables, Analytic differential equation, Regular singular point, The Cauchy-Kowalewski theorem, Zerner's 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) | |
Class Objectives /Class Outline |
We learn the basics of the theory of analytic differential equations. |
Class Schedule |
lesson1 Power series and the domain of convergence lesson2 Radius of convergence lesson3 Holomorphic functions of several variables lesson4 Cauchy's integral representation lesson5 Existence and uniqueness of solutions of analytic ordinary differential equations lesson6 Analytic continuation of solutions of ordinary differential equations lesson7 Analytic solutions of linear ordinary differential equations lesson8 Monodromy representations lesson9 Regular singular points lesson10 The Frobenius method lesson11 Initial value problem for partial differential equations lesson12 The Cauchy-Kowalewski theorem lesson13 Zerner's theorem lesson14 Bicharacteristic strip lesson15 Propagation of singularity |
Text/Reference Books,etc. |
If you can read Japanese books, please check the syllabus of this course written in Japanese. Otherwise, please consult at the classroom. |
PC or AV used in Class,etc. |
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(More Details) |
Black board |
Learning techniques to be incorporated |
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Suggestions on Preparation and Review |
Lesson1 - Lesson4 Understand fundamental properties of holomorphic functions of several variables. Lesson5 - Lesson8 Study properties of analytic solutions of analytic ordinary differential equations. Lesson9 - Lesson10 Study behaviors of solutions at singular points. Lesson11 - Lesson15 Study analyticity of solutions of analytic partial differential equations. |
Requirements |
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Grading Method |
Reports (90%), Class participation (10%). |
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. |