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.


  • 3
    $\begingroup$ Of course in a strict sense this is Ahlfors. $\endgroup$ – user135041 May 10 '14 at 16:57
  • 1
    $\begingroup$ @Herbert: Ahlfors may not be expensive everywhere. I bought an Indian edition last week for Rs. 250 (approx. 4 USD)! $\endgroup$ – Prahlad Vaidyanathan May 10 '14 at 17:00
  • 2
    $\begingroup$ @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. $\endgroup$ – Prahlad Vaidyanathan May 10 '14 at 17:17
  • $\begingroup$ Here is a textbook that is freely available online: people.math.gatech.edu/~cain/winter99/complex.html $\endgroup$ – Rudy the Reindeer May 10 '14 at 18:30

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


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.

  • $\begingroup$ Thank you for the recommendations! Are thee any references in addition to these books that you recommend as well? $\endgroup$ – OpieDopee May 10 '14 at 17:12
  • 1
    $\begingroup$ Two more, Conway's Functions of One Complex Variable and Stein/Shakarchi's Complex Analysis - but these are graduate level textbooks, so be warned. $\endgroup$ – Prahlad Vaidyanathan May 10 '14 at 17:13
  • $\begingroup$ Also Ablowitz Complex variables: introduction and applications. $\endgroup$ – auxsvr May 10 '14 at 19:58

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


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.