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10902複變數函數論Complex Analysis


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....
        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.

        Text Books 
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.
        Teaching Method 
Lecture and assignments.
It will be announced in the first class.


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