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Aryabhatta
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Book Recommendations  
« on: Jan 3rd, 2006, 10:08pm »
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Could the gurus here please recommend good books (both introductory and advanced, single/multiple variable) for learning Complex Analysis?
 
Maybe we can make this topic sticky later and provide it as a resource to future learners.  
 
Thanks.
« Last Edit: Jan 3rd, 2006, 10:09pm by Aryabhatta » IP Logged
Icarus
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Re: Book Recommendations  
« Reply #1 on: Jan 4th, 2006, 5:28am »
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The text I used was "Complex Analysis" by Lars V. Ahlfors ("An Introduction to the Theory of Analytic Functions of One Complex Variable").
 
The text is suitable for a senior undergraduate or first year graduate class (it may be a bit too abstract for earlier courses). According to others, though, it is one of the harder CA books to understand. However, it does have a really thorough discussion of the fullest form of Cauchy's theorem.
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Michael Dagg
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Re: Book Recommendations  
« Reply #2 on: Jan 11th, 2006, 11:50pm »
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There are a number of good books on complex variables that can be mentioned but their popularity generally makes most of grade when it comes to choice. In fact, there a few books that are not so popular that a pretty good.  
 
The Ahlfors book that Icarus mention is essentially one of the bibles on introductory complex analysis, and, in fact, it may not be, depending on your background, introductory at all. You will find it to be the text of choice at the more prestigious schools, so to speak, but that largely has to do with the mathematical maturity required for it. One will definitely need a solid background in real analysis which includes a working knowledge of various measures and metric spaces, and if you know any topology it will be quite helpful.
 
A second most popular text is by Brown & (Ruel) Churchill (Complex Analysis w/ Applications) which is pretty mainstream book and has been a around for many years. It is widely used and ranks well and has high visibility at many of the state universities and polytechnic schools. Churchill wrote a number of books, including one on calculus that never did gain any popularity, but he wrote some other good books, namely on operational mathematics (transforms etc.) that are popular supplements.  
 
Another book that is really not that basic at all,  but still popular, is Basic Complex Analysis by Marsden. Actually, it is a pretty hard book since most of the development is embedded in the problems instead of the body of the book.
 
The all time book with somewhat less sophistication but modeled around the standard calculus sequence is the book by Safe and Snider, Complex Analysis. It provides a pretty smooth flow from the usual calculus sequence into complex analysis without the requirement for advanced calculus or real analysis. It is widely used throughout many engineering sequences.
 
The book by Needham entitled Visual Complex Analysis is a good book for visualization but when it really comes down to a solid course it falls short.  
 
As for advanced books some of the more classic which you can Google are by Hines, Rudin, Beals, Conway, Stein, Burckel, and Krantz.
 
I can't leave without mentioning the book by Serge Lang which was not very popular but definitely has its place in history. If you like to work with algebraic structures then Lang's book will fit right in. Lang does an excellent job of initiating a nice picture of complex analysis from an algebraist point of view and in doing so provides some very useful techniques that continue consistently throughout.
 
 
 
« Last Edit: Jan 11th, 2006, 11:55pm by Michael Dagg » IP Logged

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Michael Dagg
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Re: Book Recommendations  
« Reply #3 on: Jan 12th, 2006, 2:20pm »
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I'm rather isolated mathematically these days, and CA was not my specialty, so I am not familiar with the other texts that Michael mentions. Ahlfors is not quite as bad as he makes out, though - at least the third edition wasn't. There are no measures mentioned in it, and very little little in the way of metric spaces other than C. However, a solid understanding of point-set topology is definitely helpful in following many of the arguments.
 
But then, if you don't already have a solid grasp on point-set topology, I strongly suggest investigating that subject first. Topology is the lynch-pin for all analysis and geometry. It is a subject that should be taught early in a mathematical education, because it is so widely applicable, and opens numerous doors for investigation.
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Re: Book Recommendations  
« Reply #4 on: Feb 8th, 2006, 3:06am »
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The book by Alan Beardon - Complex Analysis: The argument principle in analysis and toplogy  is also a very good book. Its very geometric, so might be a good read. I would definitely recommend any of his books.
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Re: Book Recommendations  
« Reply #5 on: Dec 12th, 2007, 3:35pm »
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My teacher used the Brown and Churchill book. I liked it, as I found the presentation very easy to understand. I think it is a good introductory treatment of the subject.
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Re: Book Recommendations  
« Reply #6 on: Oct 9th, 2011, 8:12am »
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Ok, but there is any books for beginner about solving problems/riddles ?
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Re: Book Recommendations  
« Reply #7 on: Apr 13th, 2014, 12:01am »
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"Course Material for Metric Spaces and Complex Analysis"
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Re: Book Recommendations  
« Reply #8 on: May 3rd, 2014, 11:59am »
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Thanks for this  Smiley
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Re: Book Recommendations  
« Reply #9 on: May 3rd, 2014, 12:00pm »
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and if you Have  books for beginner it will be very Ok
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JaneBD
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Re: Book Recommendations  
« Reply #10 on: Aug 6th, 2014, 9:18am »
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Try - Conway, "Functions of One Complex Variable I
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Re: Book Recommendations  
« Reply #11 on: Sep 29th, 2014, 12:49pm »
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on Dec 12th, 2007, 3:35pm, william wu wrote:
My teacher used the Brown and Churchill book. I liked it, as I found the presentation very easy to understand. I think it is a good introductory treatment of the subject.

 
Our introductory book was the same; and I too, had the same experience.
 
+1.
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Re: Book Recommendations  
« Reply #12 on: Nov 5th, 2014, 9:49am »
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to learn the complex analysis i think visual complex analysis by the needham is the good and  i think is the best
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gitanas
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Re: Book Recommendations  
« Reply #13 on: May 27th, 2016, 5:07am »
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Iain Banks - The Wasp Factory
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