• A-
• A
• A+
03-5715131#35401 mengfen@mx.nthu.edu.tw 吳小姐

Title

Video

Syllabus

## 章節大綱

L14A
Carathéodory定理
0:00 A bound for the real part of f cannot imply a bound for
the modulus of f. f的實部無法控制f的絕對值
6:09 Carathéodory's Theorem Carathéodory定理
9:48 An Entire Function Having Bounded Real Part Is a
Constant 實部有界的整函數為常數函數
11:35 Proof 證明
14:53 Proof of Carathéodory's Theorem Carathéodory
定理的證明

L14B

Carathéodory定理、調和函數
0:00 Proof of Carathéodory's Theorem (cont.)
Carathéodory定理的證明 (續)
12:42 Harmonic Functions 調和函數
21:00 Complex Structure 複結構

L14C

0:00 Complex Structure (cont.) 複結構 (續)
2:46 Real and Imaginary Parts of a Holomorphic Function
Are Harmonic 解析函數的實部和虛部都是調和函數
5:49 Existence of Harmonic Conjugate 調和共軛的存在性
11:16 Finding Harmonic Conjugate (Locally)
尋找調和共軛 (在局部)
15:03 Example 例題

L14D

0:00 Finding Harmonic Conjugate (On a Simply Connected
Domain) 尋找調和共軛 (在單連通域)
2:36 Proof 證明
10:53 Finding Harmonic Conjugate (Quick Method)
尋找調和共軛 (比較快的方法)
24:20 Example 例題

### 課程資訊

• #### 程守慶 教授

• 上架日期: 2023-07-19
• 點閱次數: 4652