Best complex analysis references?

Question

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!

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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.