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FOR BEGINNERS:

Currently, I am looking for a textbook on complex analysis, which covers complex analysis from the beginning, and majorly focuses on contour integration, and the residue theorem.

On SE I have seen people use contour integration to solve sums, integrals, but I never got the hang of it, so I would like a book which explains residue theorem, contour integration etc..

Suggestions are welcome!

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I liked the free book:

"A first Course in Complex Analysis" by Matthias Beck, Gerald Marchesi, Dennis Pixton, which consists of plenty of exercises and hints/solutions.

Available at: http://math.sfsu.edu/beck/complex.html

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Schaum's Outline in Complex Variables LINK

Starts from the beginning. Contains a whole chapter on integrals by contours. If you can do all the problems at the end of that chapter, you will be ready to tackle problems here!

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  • $\begingroup$ I am considering this, do you have any experience with this? $\endgroup$ – Amad27 Dec 21 '14 at 15:13
  • $\begingroup$ Also does it contain residue theorem, and its applications to sums and integrals? $\endgroup$ – Amad27 Dec 21 '14 at 15:15
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Churchill's text is quite computational and focuses on the topics of your interest. But if you are math major, you should definitely read either Stein or Ahlfors sooner or later.

http://www.amazon.com/Complex-Variables-Applications-Brown-Churchill/dp/0073383171

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I own a copy of Gamelin which was my prescribed complex analysis text. Very good, geometric point of view but still with all the Cauchy integration you're after. All the content needed for undergrad and some GRE stuff too.

EDIT: Here is a link to a pdf

https://thunhan.files.wordpress.com/2008/08/complex_analysis_t_gamelin.pdf

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I'd recommend the second book in the "Princeton Lectures in Analysis" series. It's titled Complex Analysis, written by Elias Stein and Rami Shakarchi.

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    $\begingroup$ For beginners? Really? Stein does not focus on the computation of contour integrals and applications of residue theorem. $\endgroup$ – Mark Fantini Dec 21 '14 at 12:57
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    $\begingroup$ Although the book doesn't focus on computational stuffs, it's appropriate for beginners. $\endgroup$ – Math.StackExchange Dec 21 '14 at 13:05

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