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Lars V. Ahlfors
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Complex Analysis 3rd Edition

by Lars Ahlfors (Author)
4.4 4.4 out of 5 stars 247 ratings
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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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  1. ISBN-10
    0070006571
  2. ISBN-13
    978-0070006577
  3. Edition
    3rd
  4. Publisher
    McGraw-Hill Education
  5. Publication date
    January 1, 1979
  6. Language
    English
  7. Dimensions
    6.3 x 1 x 9.1 inches
  8. Print length
    336 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ McGraw-Hill Education; 3rd edition (January 1, 1979)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 336 pages
  • ISBN-10 ‏ : ‎ 0070006571
  • ISBN-13 ‏ : ‎ 978-0070006577
  • Item Weight ‏ : ‎ 1.3 pounds
  • Dimensions ‏ : ‎ 6.3 x 1 x 9.1 inches
  • Customer Reviews:
    4.4 4.4 out of 5 stars 247 ratings

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Lars V. Ahlfors

Lars V. Ahlfors

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Customer reviews

4.4 out of 5 stars
4.4 out of 5
247 global ratings

Top reviews from the United States

Paul Bonyak
5.0 out of 5 stars The standard for modern treatment of complex analysis
Reviewed in the United States on August 3, 2014
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Classic 1st year graduate text which emphasizes treatment by the methods of elementary topology. An approach you should feel comfortable with if you used Rudin's Principles 3rd edition. In fact the first seven chapters of Rudin constitute better than adequate preparation for this text. The older British texts emphasized the manipulation of power series which is certainly suited to solution of differential equations and development of the transcendental functions-Whittaker and Watson is the standard here. It should be noted that the topological methods were abstracted from these older methods and made systematic. This modern approach at the very least accomplishes the same ends with less clutter and more economy of reasoning. An example of what you'll find not typically done in analysis texts but proved here is that a metric space is compact if and only if every infinite sequence has a limit point (chapter 3). This text by a great mathematician ranks like Rudin as another "how to think like a mathematician" text.
14 people found this helpful
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the-king-likewise-says
5.0 out of 5 stars Great textbook by revered master in the field
Reviewed in the United States on December 17, 2017
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This is an excellent and classic treatment of complex analysis. The treatment is comparatively modern and uses the language of point set topology throughout. However, the author takes pains to develop geometric intuition whenever feasible, without letting the intuitiveness result in a decrease in standards or rigor. This textbook will require a good deal of mathematical maturity, although somewhat more classical in presentation, the book probably requires a bit more mathematical maturity than the modern standard by Stein and Shakarchi. The exercises look challenging, but slightly more staightforward than Stein and Shakarchi. This book should be read for the way a true towering figure in the field of complex analysis thinks about it and transmits it to beginners.
10 people found this helpful
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Mulling
5.0 out of 5 stars This book is a *slow burn*, but probably the best you'll ever see
Reviewed in the United States on May 16, 2014
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His style takes some getting used to.
The top of every chapter might seem like an informal invitation- but don't let him seduce you too far there!
Ahlfors can be a little bit "sing-songy", but that just because he's an inspired teacher.

So the burden is on the *reader*.

For the new student: Sorry, but it requires translating every sentence from old-fashioned into sentences that use logical quantifiers.

Ahlfors typically writes "...unless we see that...", " except if such and such...", "...so long as ..." ,"...if it's the case that...", etc. to suit the flow of the text.

*Don't* get wrapped up in the beauty of his language, and *Do* verify every single sentence in the book.
6 people found this helpful
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dc
4.0 out of 5 stars Mixed feelings
Reviewed in the United States on April 25, 2014
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Opinions on this book seem split down the middle. On one side, it is a classic and contains many great topics regarding a fascinating field of mathematics. Ahlfors proofs are slick (though sometimes too slick) and reading this book (most of the time) is a joy. However, I only read it as supplement to a different text. Ahlfors could be frustrating to read for some; it's not particularly well laid out, and proofs do not have a definite beginning or end. He is prone to discussing and then recapitulating the discussion as a theorem, where the proof is buried somewhere within the discussion. There are also too few exercises, most always less than 10 per section, though the ones offered are usually ripe. Overall I enjoy having this book, and will refer back to it in the future.

One series drawback is the price. Buy a used copy! Spending this much (almost $200 at the time of writing) is absurd, especially for such a slim book. It's a classic and well deserving of that title, there are probably better books out there, but anyone seriously interested in complex analysis should own a copy of Ahlfors.
10 people found this helpful
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Amazon Customer
5.0 out of 5 stars Five Stars
Reviewed in the United States on March 7, 2018
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It is exactly as expected and came too early than I was expecting. Thanks...
One person found this helpful
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alvaro ortiz
5.0 out of 5 stars The book is not a begginers book, it goes ...
Reviewed in the United States on March 20, 2015
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The book is not a begginers book, it goes straight to the important stuff and leaves many details to the reader. still a must have book.
2 people found this helpful
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Mick Twohig
3.0 out of 5 stars Pages a little on the thin side, but the price is a sweetener
Reviewed in the United States on July 24, 2019
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Content is fine. The paper is on the thinner side however, so you can see content from the other side of the page. Not a major issue, but can be tiring on the eyes if you’re reading for an extended period. However, for the price, maybe the thinner paper is an acceptable tradeoff for some. I’ll live with it.
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Xu Shichen
5.0 out of 5 stars Indian Edition? Works!
Reviewed in the United States on March 23, 2014
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I didn't thought it would be the Indian Edition, and had some doubt when I first receive it. Literally no difference from the US edition. Works well!
3 people found this helpful
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Top reviews from other countries

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Iuri
5.0 out of 5 stars Ótimo livro
Reviewed in Brazil on July 21, 2023
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Livro muito bem escrito, apenas poderia dar alguma ênfase a mais para teoria analítica dos números. Entregue em perfeito estado
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Rishabh
5.0 out of 5 stars Best book.. for complex analysis
Reviewed in India on May 30, 2021
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Best book.. for complex analysis , must read book for mathematics student.
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J.C.
4.0 out of 5 stars Good book, but not an excellent printing
Reviewed in Mexico on June 4, 2020
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Its content is good, even though it is difficult to read for a beginner. The content of this indian version is the same as the original one.
The quality of the printing is acceptable but not excellent, some pages have marks that make them look like they're copies instaed of an original printing.
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Amin
5.0 out of 5 stars Great
Reviewed in Canada on May 20, 2019
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Arrived very quickly, in great condition. The print is not perfect, but great for the price.
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Amazon Customer
5.0 out of 5 stars Great book.
Reviewed in the United Kingdom on November 2, 2017
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Great book.
Be careful with the customs.
One person found this helpful
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