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特藏,數學,統計
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10902複變數函數論

2021-02-01-2021-06-30

國立清華大學 數學系 程守慶

關鍵字: 複變數函數論(Complex Analysis) 解析函數(holomorphic function) 柯西積分公式(Cauchy integral formula) 最大模數原則(maximum modulus principle) 調和函數(harmonic function) 保角映射(conformal mapping).

This course will cover the concept of holomorphic functions, Cauchy's integral formula. Maximum modulus principle for holomorphic functions shall be proved....
 
  
【課程說明】
        Course Description

Basically we shall cover the following topics.
(1)Cauchy-Riemann equation,Cauchy theorem for holomorphic functions,
(2)Cauchy integral formula,
(3)Maximum modulus Principle,
(4)Laurent series,meromorphic functions,
(5)Calculus of residues,
(6)Harmonic functions of two real variables,
(7)Conformal mappings, Riemann mapping theorem.
  
  
 

【指定用書】
        Text Books 
  
 
 
【參考書籍】
        References
1L. V. Ahlfors: Complex Analysis,
2E. M. Stein and R. Shakarchi: Complex Analysis, Princeton University Press.
3.R. E. Greene and S. G. Krantz: Function theory of one complex variable,

John Wiley & Sons, INC.
4.W. Rudin: Real and Complex Analysis, McGraw-Hill Book Company.
  
 
 
【教學方式】
        Teaching Method 
Lecture and assignments.
 
 
【成績考核】
        Evaluation  
It will be announced in the first class.

 

 
 
 
課程版書 . 作業   .   新書分享
 

 

前往課程 View Course
https://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=289&
https://www.youtube.com/playlist?list=PLS0SUwlYe8cznK63NIQBrpljztalHNGsZ