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I want a really good book on Complex Analysis, for a good understanding of theory. There are many complex variable books that are only a list of identities and integrals and I hate it. For example, I found Munkres to be a very good book for learning topology, and "Curso de Análise vol I" by Elon Lages Lima is the best Real Analysis book (and the best math book) that I have read with many examples, good theory and challenging exercises.

An intuitive and introductory approach is not very important if the book has good explanations and has correct proofs.

Added: If it is possible, tell me your experience with your recommended books and if you got a really good understanding of complex analysis with a deep reading.

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    @GastónBurrull I do not like analysis. I am past under graduation. But I want to give it a try if I can find some gem of a book, otherwise I guess its too late for me..2014-11-05

16 Answers 16

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An Introduction to Complex Analysis by Ravi P. Agarwal , Kanishka Perera , Sandra Pinelas is a fantastic book!

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My biggest recommendation is Tristan Needham's Visual Complex Analysis. Although not a strict textbook, all of the traditional theorems in elementary complex analysis are covered. Proofs aren't thorough, but are instead explained geometrically in general outlines. The big advantage with this book is the massive amount of pictures, nearly on every page in some sections.

Other great classics are Rudin's Real and Complex Analysis, Conway's Functions of One Complex Variable. For a thorough but relatively intuitive approach, I also heavily recommend Sarason's Complex Function Theory.

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    I think that Tristan's book is not the book that I was looking. But Conways looks good. What about Rudin, which topics cover it?.2012-06-19
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Conway, "Functions of One Complex Variable I" http://books.google.ca/books?id=9LtfZr1snG0C

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    I've always felt Conway was overrated. It's ok,but pretty dry and it misses a lot of the beautiful geometry of the complex plane. It's probably the second volume that really impressed most people-the material in THAT book isn't readily available in a lot of sources.2013-08-27
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The followings are very, very good. Note that you should start with the first one if you are a beginner.

  • Reinhold Remmert. Theory of complex functions. Springer 1991.
  • Reinhold Remmert. Classical topics in complex function theory. Springer 2010.
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    thanks for your proper material =)2012-06-19
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The books below are excellent:

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    I haven't seen either,but I'm told Ulrich is outstanding.2013-08-27
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A very classic book to learn complex analysis from is Ahlfors's book (which I used). There is also Stein and Shakarchi's book, and Bak and Newman's book.

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    @Gaston NO,Gaston,it's NOT a good book. It's just been enshrined by people who had the misfortune of being graduate students when there weren't a lot of choices for textbooks at that level.That and Ahlfors was one of the preeminient function theorists of the 20th century-which creates a lot of misplaced reverence. The third and final edition was a VAST improvement over the first-which was an unreadable abomination-but still not a great book by any means.2013-08-27
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Here's one that I love: Donald Sarason's book, Complex Function Theory. It's beautifully and economically written, so that it really flows. It was published by Henry Helson in his garage for a long time, but has been taken over by the American Math. Soc.

It covers complex analysis up to and including some advanced topics such as the Riemann mapping theorem, starting from basic real analysis.

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    It's a bit terse for my tastes, but I agree,this is quite a nice book if that's your cup of potion.2013-08-27
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I had really good luck with Fisher's Complex Variables and Gamelin's Complex Analysis.

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    +1 for 2 great books. The former is a classic in a wonderful cheap Dover edition and the latter is on it's way to becoming a classic. My one quibble with Gamelin is that it tends to be a little TOO soft for a graduate course at times, especially early in the book. But that's what makes it ideal for self study. It really starts from jump,unlike most books-even honors high school students could use the early chapters!2013-08-27
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Ahlfors, Complex Analysis. It is an absolute classic and, while spartan-seeming, is a fantastic introduction to the course. It was actually my second introduction to the subject (I had it at an earlier undergraduate level using Churchill & Brown, which isn't bad, but no classic.) That book, coupled with an amazing instructor, made a huge impact.

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Look up this free complex analysis book by Shabbat http://math.stanford.edu/~ryzhik/shabat-all.pdf

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Elias Wegert's book: Visual Complex Functions: An Introduction Using Phase Portraits might not be so good for analytic techniques, but I've found it to be really good for honing one's intuition. (it's the first of a planned two volume set).

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I think Serge Lang's book on Complex Analysis is a good a one to go with.

http://www.amazon.com/Complex-Analysis-Graduate-Texts-Mathematics/dp/0387985921

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No one has mentioned here, but 'A First Course in Complex Analysis with Applications' by zill is my favourite book. It is so clear and comprehensive, and much simpler and intutive explainantions.

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    From the authors taste in Munkres, I expect he was looking for a graduate book. However, I did use this book as an undergraduate. I do still have Zills book on DE too.2014-11-04
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as my opinion s.ponnusamy ''foundation of complex analysis'' is the best book. same concepts are taught in simple and different way.

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Complex Analysis by Kunihiko Kodaira

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Complex Analysis, by Beardon is unmatched in quality. I put it above Ahlfors, because in the preface of Ahlfors CA, Allen F Beardon is mentioned with gratitude.

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    I've never seen that book! How could Beardon have written a complex analysis text and I didn't know?2016-01-14