A Classic
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Another classic text from graduate school (text for class taught by P.L. Duren) providing a background in introductory complex analysis. This book is nicely written with some elegant exploration of the motivations and backgound for a number of the central concepts. This may be surprising given the physical slimness of the text (I noticed elegance of the exposition and attention to motivation on a recent reread of some of the book after nearly twenty years -- I had not remembered this exposition, perhaps because the reading in graduate school was not quite as "liesurely" (unless "fear driven" and "pressured" are synonyms for "liesurely"). The theory topics are nicely covered -- if, however, you are an engineer looking for methods of calculating complex intgral there are other texts.
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A good and valuable intro to Complex Analysis
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I picked up this book as a text to my complex functions class. The topics presented in the book is the classic need-to-know materials for undergraduates (complex functions, analytic functions as mappings, complex integration, series and products, etc), plus other topics which undergraduate complex analysis course usually omits: Weirstrass theory, Picard's theorem and zeta function (in a complex analysis point of view). The presentation is clear, the mathematic is well presented (but with a few gaps in the proofs), the examples are motivated and useful and the exercises are ok (some of them are pretty challenging!). The book should serve as a text very well. PS: Lars V. Ahlfors was the first recipient of the Fields Medal (in 1936, along with Jesse Douglas).
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$143?!?!
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This is a classic complex analysis text, a pleasure to read and covering all the usual topics. The prerequisites are modest; ideally, one will be familiar with the material in Rudin's "Princples of Mathematical Analysis," but a good, mathematically oriented calculus course (Spivak's "Calculus" is beautiful) is quite sufficient. That said, the price tag is ridiculous. It was bad enough at $90 (judging by previous reviewers, that was back in the ancient days of 2001). The last edition of this book is dated 1979. It's used in graduate courses all around the world. That means that used copies are not hard to come by. For $143, one can buy a used copy of Ahlfors, and *new* copies of Conway's and Needham's complex analysis books, and still have pocket change left. That's the course I would recommend.
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If you can spend $90, you should buy something else.
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I quite agree with the reviewers from Minneapolis, Denver, Stockton and Thessaloniki. True, Ahlfors was THE book on complex analysis (better known as "theory of functions" then) some thirty to forty years ago. But I can see no point in using it as a textbook now. As there are many good treatments on the subject today, it is high time we waved a farewell to this book. I recommend Cartan's book published by Dover since it is available for only twelve dollars.
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A Fantastic Book!
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If you have already had a little exposure to complex analysis, I believe this is a great book to read. Instead of calculating lots of useless contour integration examples, it concentrates on explaining why things are the way they are. As an example, look at the sections on the Gamma and Zeta functions.
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