Which book on complex analysis is good for self study?

I am an average student and have just a very basic knowledge of this subject. I want to cover up to Runge's Theorem.

I heard about few books- Gamelin's Complex Analysis; a text by Churchill and another Ahlfors' Complex analysis.

Thank you.

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    $\begingroup$ I like Ahlfors' a lot. $\endgroup$ – Tunococ Sep 10 '13 at 0:37
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    $\begingroup$ @SaraTancredi: Maybe review these two postings: math.stackexchange.com/questions/30749/… and math.stackexchange.com/questions/419439/…, Regards $\endgroup$ – Amzoti Sep 10 '13 at 0:41
  • $\begingroup$ Thank you Tunococ and Amzoti. $\endgroup$ – Sara Tancredi Sep 10 '13 at 1:23
  • $\begingroup$ OFF: good luck; I found math self-study incedibly hard, especially in English, which is a foreign language for me. $\endgroup$ – Zoltán Schmidt Sep 10 '13 at 19:52
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    $\begingroup$ @ZoltánSchmidt But I find self study more interesting. Actually, your English is not bad. Look, you are writing very well. The problems is that you are indulged in many other extra curricular activities :) $\endgroup$ – Sara Tancredi Sep 11 '13 at 2:23

Gamelin is quite good. After or together with it, I recommend you to read the following.

  • Reinhold Remmert. Theory of complex functions. Springer 1991.

Then there is the second volume:

  • Reinhold Remmert. Classical topics in complex function theory. Springer 2010.

Nice link ;)

  • Visual Complex Analysis (Tristan Needham)
  • Visual Complex Functions:An introduction with phase portraits (Elias Wegert)

Enjoy Them...

  • $\begingroup$ I've also downloaded these texts. they look cool. Thanks Ricardo. $\endgroup$ – Sara Tancredi Sep 11 '13 at 2:14

Gilman, Kra and Rodriguez, wrote the excellent book "Complex Analysis in the Spirit of Lipman Bers". It has everything you need to study complex analysis and has great exercises.


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