| Academic Year |
2026Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB282000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析学Ｂ |
Subject Name
（Katakana） |
スウリカイセキガクB |
Subject Name in
English |
Mathematical Analysis B |
| Instructor |
HIRATA KENTARO |
Instructor
(Katakana) |
ヒラタ ケンタロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Tues7-8,Weds5-6：SCI E208 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Lecture, Blackboard |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
B
:
Japanese／English |
| Course Level |
4
:
Undergraduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
Senior students in Department of Mathematics |
| Keywords |
|
| 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）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. |
|---|
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. If time permits, the proof of the Riemann mapping theorem is given. |
| Class Schedule |
lesson1 Basic properties of harmonic functions(1)
lesson2 Basic properties of harmonic functions(2)
lesson3 Poisson integral and Dirichlet problem on the disk
lesson4 Characterizations of harmonic functions and removable isolated singularities
lesson5 Harnack theorems
lesson6 Bounded harmonic functions on the disk
lesson7 Lindelof theorem for holomorphic functions
lesson8 Bocher theorem
lesson9 Upper/Lower semicontinuous functions
lesson10 Basic properties of sub/super harmonic functions
lesson11 Equivalent conditions for sub/super harmonicity
lesson12 Approximation and regularization of sub/super harmonic functions
lesson13 Dirichlet problem and Perron solution
lesson14 Regular boundary points and the boundary behavior of Perron solutions
lesson15 Riemann mapping 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 |
Post-class Report |
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. |