Complex analysis is one of the most central subjects in
mathematics. It is compelling and rich in its own right, but it is
also remarkably useful in a wide variety of other mathematical
subjects, both pure and applied. This book is different from others
in that it treats complex variables as a direct development from
multivariable real calculus. As each new idea is introduced, it is
related to the corresponding idea from real analysis and calculus.
The text is rich with examples and exercises that illustrate this
point. The authors have systematically separated the analysis from
the topology, as can be seen in their proof of the Cauchy
theorem.The book concludes with several chapters on special topics,
including full treatments of special functions, the prime number
theorem, and the Bergman kernel. The authors also treat $H^p$
spaces and Painleve's theorem on smoothness to the boundary for
conformal maps. This book is a text for a first-year graduate
course in complex analysis. It is an engaging and modern
introduction to the subject, reflecting the authors' expertise both
as mathematicians and as expositors.
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