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I have a complex analysis test in 15 days. I have never studied the subject before. The only analysis I know is the first 7 chapters of baby Rudin. I plan to learn some multi-variable analysis and then start complex analysis. I have Rudin's Real and Complex Analysis and Complex Analysis by Lars Ahlfors, but they seem like books that would take a lot of time to study. I'm looking for a book with really simple proofs, yet ones which cover a decent bit of ground. The easiest book I have read so for is Real Analysis by Robert Bartle. Can someone suggest a book for complex analysis which is as easy as Bartle? Thanks.

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    $\begingroup$ Complex analysis is a fairly large subject. Can you be a bit more specific? $\endgroup$ – Chappers Apr 14 '17 at 13:45
  • $\begingroup$ See math.stackexchange.com/a/160143/589. $\endgroup$ – lhf Apr 14 '17 at 13:46
  • $\begingroup$ The topics I have for my test are analytic functions, cauchy's theorum, cauchy's integral formula, max modulus principle , laurent series, singularities, theory of residues, contour integration, $\endgroup$ – tony Apr 14 '17 at 13:48
  • $\begingroup$ Not sure if you can do it in 15 days, but Basic Complex Analysis by Marsden&Hoffman is a good book for beginners, it's straightforward and gets into complex line integrals & Cauchy's integral theorem in just the second chapter. I wouldn't recommend rushing complex analysis, but if you just want to pass the test you're good with that i think. $\endgroup$ – Renormaliser137 Apr 14 '17 at 13:49
  • $\begingroup$ @Dimitris, I will check it out. Would what I learnt in rudin be enough as prerequisites? $\endgroup$ – tony Apr 14 '17 at 13:50
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When I took the course a few years ago, the notes of Ash and Novinger were recommended to me as they are designed to be gone over in a compressed time period. So they might be a good thing to look at. They are available online at:

http://www.math.uiuc.edu/~r-ash/CV.html

Then use Rudin and Ahlfors for additional exercises. There are many solution manuals to Rudin available online, and many of the problems are discussed on Stack Exchange if you look for them.

Best,

--Kris

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