Customer Reviews

Analytic Function Theory, Volume I (AMS Chelsea Publishing)

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This book is by an outstanding master of the subject and a fine writer in the classical style. Hille treats the subject in detail, with many examples and historical references, but does not dumb the topic down, or render it soft. His treatment is more complete than many others for the serious beginner, since he proves such theorems as the one that having continuous partials satisfying the Cauchy Riemann equations implies holomorphicity, instead of just referring for this to the real variable case, which the student probably has never seen proved. He even proves a polygonal version of the jordan curve theorem in an appendix. His discussion gives the student a concrete feel for the subject by starting with serious examples such as fractional linear transformations, before going into theoretical development of integrals and power series. all that in volume I. Volume II is really thorough with a proof of the big Picard theorem, one of few places it is found in textbook form, and even some discussion of riemann surfaces of algebraic curves. this book is a great bargain and of high quality for one who wants a thorough serious treatment of analytic functions, from scratch.