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I own Gamelin's 'Complex Analysis', but I'm having a bit of a hard time understanding it. I have also tried watching MIT Open Courseware videos on the subject, but I easily get lost. Are there any references (preferably NOT textbooks as I am short on funds at the moment) that server as a smooth transition from calculus to complex analysis? I have been lucky to have some help from a user on this website, but I would also like some other references so I don't constantly take up his time.

Thanks!

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Of course in a strict sense this is Ahlfors. –  user135041 May 10 at 16:57
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@Herbert: Ahlfors may not be expensive everywhere. I bought an Indian edition last week for Rs. 250 (approx. 4 USD)! –  Prahlad Vaidyanathan May 10 at 17:00
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@Herbert: Yes, really. The publisher "Tata McGrawHill Education" has taken tp publishing Indian editions of many "standard" textbooks - cheap paperbacks, but they are a real boon for students, I should think. –  Prahlad Vaidyanathan May 10 at 17:17
    
Here is a textbook that is freely available online: people.math.gatech.edu/~cain/winter99/complex.html –  Matt N. May 10 at 18:30
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4 Answers 4

Here are some books that I would recommend (in decreasing order):

  • Needham's Visual Complex Analysis : This is a really lovely book if you want to look at pictures and waft through the basics without getting too worried about the nitty-gritty.

  • E.T. Copson's Introduction to the theory of functions of one complex variable : The book is somewhat dated, but I learnt quite a lot from it and I really liked the author's style.

  • L.V. Ahlfors' Complex Analysis : This is the bible. Never leave home without it.

  • D'Angelo's An Introduction to Complex Analysis and Geometry : These are some notes the author wrote for a course meant for "bright freshman students". It is available online here. I haven't used it myself, but it looks good to me.

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Thank you for the recommendations! Are thee any references in addition to these books that you recommend as well? –  Ethan May 10 at 17:12
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Two more, Conway's Functions of One Complex Variable and Stein/Shakarchi's Complex Analysis - but these are graduate level textbooks, so be warned. –  Prahlad Vaidyanathan May 10 at 17:13
    
Also Ablowitz Complex variables: introduction and applications. –  auxsvr May 10 at 19:58
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1) Ahlfors is the best

2) Conway's GTM11,159

3) GTM122,172

4). also, I recommend Freitag's 'complex analysis'(Spring Universitext)

5). Henri Cartan, Elementary Theory of analytic functions of one or several complex variables

6).Elias M.Stein&Rami Shakarchi, Complex analysis

7).Raghavan Narasimhan&Yves Nievergelt, Complex analysis in complex variable, second edition

8). M. A. Lavrentieff & B. V. Shabat, Methods of Functions of a complex variable, Sixth Edition

last but not least 9). Kunihiko Kodaira, Complex analysis

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You may also want to try:

Complex Analysis by Serge Lang

mainly because it has an accompanying problems and solutions manual:

Problems and Solutions for Complex Analysis by Rami Shakarchi

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Since you indicated that you need a transition from calculus to complex analysis, it would probably be best to start with an application-oriented text (i.e. no graduate-level analysis). You could try Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics.

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