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 over specialized 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. 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.

Complex Numbers, Complex functions, Analytic functions,etc.