Complex Analysis
内容简介
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.
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作者简介
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目录
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读书文摘
A continuous function on a compact set Ω is bounded and attains a maximum and minimum on Ω
Similarly, a closed set F is connected if one cannot write F = F1 ∪ F2 where F1 and F2 are disjoint non-empty closed sets.
事实上，只有解析函数或全纯函数可以自由地进行微分和积分。它们是法文“Théorie des fonctions”或德文“Funktionentheorie"意义下唯一真正的”函数"。
在球面表示中，对于加法和乘法没有简单的解释，其方便在于无穷远点不再特殊
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