| 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 |
WSA46000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析特論Ｄ |
Subject Name
（Katakana） |
スウリカイセキトクロンデー |
Subject Name in
English |
Topics in Mathematical Analysis D |
| Instructor |
HIRATA KENTARO,KAMIMOTO SHINGO,TAKIMOTO KAZUHIRO,KAWASHITA MISHIO |
Instructor
(Katakana) |
ヒラタ ケンタロウ,カミモト シンゴ,タキモト カズヒロ,カワシタ ミシオ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Tues7-8,Weds7-8：SCI B305 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Lecture, Blackboard |
| Credits |
2.0 |
Class Hours/Week |
|
Language of Instruction |
B
:
Japanese／English |
| Course Level |
6
:
Graduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
1st year of master course |
| Keywords |
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| 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) | |
|---|
Class Objectives
/Class Outline |
To acquire basic knowledge of harmonic function theory in a plane, we begin with expositions of some properties and behavior of harmonic functions, and then investigate some basic properties of sub/super harmonic functions and explain the Perron method concerning the Dirichlet problem in a general domain. In the last two lessons, we will show the Riemann mapping theorem. |
| Class Schedule |
lesson1 Basic properties of harmonic functions
lesson2 Poisson integral and Dirichlet problem on the disk
lesson3 Characterizations of harmonic functions and removable isolated singularities
lesson4 Harnack theorems
lesson5 Bocher theorem
lesson6 Bounded harmonic functions on the disk
lesson7 Upper/Lower semicontinuous functions
lesson8 Basic properties of sub/super harmonic functions
lesson9 Equivalent conditions for sub/super harmonicity
lesson10 Approximation and regularization of sub/super harmonic functions
lesson11 Construction of the greatest harmonic minorant of a superharmonic function
lesson12 Dirichlet problem and Perron solution
lesson13 Regular boundary points and the boundary behavior of Perron solutions
lesson14 Riemann mapping theorem
lesson15 Caratheodory theorem |
Text/Reference
Books,etc. |
Reference book:
[1] 相川弘明，複雑領域上のディリクレ問題－ポテンシャル論の観点から，岩波書店
[2] T. Ransford，Potential Theory in the Complex Plane，Cambridge University Press
[3] S. Axler, P. Bourdon, W. Ramey，Harmonic Function Theory，Springer
|
PC or AV used in
Class,etc. |
|
| (More Details) |
Distribute some prints if necessary. |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Review what you learned in each lesson with lecture notes and handouts. |
| Requirements |
|
| Grading Method |
Based on report 70% and class participation 30% |
| 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. |