Complex Analysis | 
 enlarge | Author: Lars Ahlfors
Publisher: McGraw-Hill Science/Engineering/Math
Category: Book
Buy New: $98.00
New (14) Used (9) from $70.00
Rating:  20 reviews
Sales Rank: 158291
Media: Hardcover
Edition: 3
Pages: 336
Number Of Items: 1
Shipping Weight (lbs): 2.5
Dimensions (in): 8.9 x 5.9 x 0.9
ISBN: 0070006571
Dewey Decimal Number: 515.93
EAN: 9780070006577
Publication Date: January 1, 1979
Availability: Usually ships in 1-2 business days
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Product Description
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 overspecialized 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, and 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. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.
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| Customer Reviews: Read 15 more reviews...
 A good and valuable intro to Complex Analysis February 28, 2004
bal gombak (Cambridge, MA USA)
14 out of 16 found this review helpful
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 (from 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).
Essential May 2, 2001
5 out of 5 found this review helpful
How can anyone fail to read this book? The exposition is rigorous, coherent, precise without being either pedantic or overwhelming. A certain level of mathematical maturity is requisite, such as one might acquire in the course of digesting Rudin's "Principles of Mathematical Analysis" or Apostol's book. This is not a compendium of results and exercises for engineers or physicists, it is a concise introductory text in pure mathematics. In that sense it is too abstract and proof oriented for that aforementioned audience which would be better served by a text in mathematical methods. Even pure mathematics students would benefit from supplementing this book with more detailed, computationally oriented books such as Conway or Boas. It's unrealistic to expect to find everything in one text and to further expect it to remain cogent and approachable. Ahlfor's beautiful little book has justifiably remained a classic for four decades.
A Classic Masterpiece June 15, 2000
Eze (Valencia, Spain)
11 out of 11 found this review helpful
This book has been, since its first edition in 1953, the standard textbook for rigorously learning complex analysis, and not without a reason. The wonderful theory of this branch of mathematics is appropriately emphasized and thoroughly constructed, leading to more general and precise results than most textbooks. While the constant appearance of new texts on the field can only help appreciate the subject from a different perspective, few give you such a deep and serious treatment like this gem.Postscript: An earlier reviewer claims that Ahlfors never defines the set of complex numbers, while this is indeed done in the fourth through sixth pages in a much more analytical way than generally found elsewhere. It is quite possible to dislike this author's style or approach (or anybody's for that matter), but it would be difficult to charge Ahlfors with being sloppy with his writing.
Classic book on complex analysis: one of the best, but overpriced December 25, 2007
Alexander C. Zorach (New Haven, CT)
1 out of 1 found this review helpful
This book is a classic on complex analysis. Unlike some "classics" in mathematics, it is quite accessible, for students at the appropriate level. In order to understand this book, one would need a solid background in mathematical analysis/advanced calculus, and probably one prior course in complex analysis.
This book is concise but reads rather quickly, at least compared to other books that are similarly dense. I think Ahlfors is a very good writer. Although this book seems thin, it covers a lot of material. I find the order of the material to be quite natural. I also like the problem sets...they are not too difficult for a book at this level, and they are very well-designed to help reinforce the basic ideas as well as explore deeper questions.
I think this book would make an outstanding textbook for a graduate course in advanced calculus. However, there are also a number of more modern textbooks on the subject (Greene & Krantz) that would also make equally good textbooks, so the choice of a book is more a question of personal taste than anything else. As a more introductory book on the same topic, I would recommend a number of books, including the one by Churchhill, or at a more intermediate level, the one by Gamelin, or the book by Stein and Shakarchi. There are other good complex analysis books out there too. The book by Hahn is also worth looking at--it is far more thorough than this book, although both the style of writing and the typesetting are a little less clear. Price-wise, however, these other books might offer more value for your money than this classic text.
A Classic June 17, 2004
ktrmes (New York, New York USA)
6 out of 7 found this review helpful
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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