Emphasizing how complex analysis is a natural outgrowth of multivariable real calculus, this graduate textbook introduces the Cauchy integral formula, the properties and behavior of holomorphic functions, harmonic functions, analytic continuation, topology, Mergelyan's theorem, Hilbert spaces, and the prime number theorem. The third edition clarifies many of the later proofs. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)