# Introductory books on complex analysis? [duplicate]

I'm a senior in my undergrad. years of college, and I haven't taken Complex Analysis yet.

I have taken Real Analysis I (covered properties of $\mathbb{R}$, set theory, limits of sequences and functions, series, (uniform) continuity, uniform convergence) and Abstract Algebra I (covered $\mathbb{Z}_{n}$, an intro to group theory (groups, subgroups, quotient groups, isomorphism theorems, semidirect products), and an intro to ring theory (fields, ideals)).

The book that we use at the university I attend isn't very analytical, from my understanding. (The book is Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd ed. by Saff.) Of the courses I've taken in my undergrad, Real Analysis I has definitely been my favorite course so far, and I will be taking Real Analysis II (covers integration and differentiation in $\mathbb{R}^n$, Riemman-Stieltjes, and some other topics that I don't know about) this upcoming fall.

Are there any books on complex analysis that you would suggest given my background? Thank you!

Edit: Other courses I have taken: I have taken Calculus I through III (nothing on Differential Equations - although I do know what a first-order linear differential equation is), actuarial science courses (Probability (Calculus-based), Statistics (Calculus-based), Life Contingencies), and Linear Algebra (one semester using Larson's Elementary Linear Algebra and a second semester independent study using Axler).

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@GitGud I'm assuming he has calculus integration, just not the "formal" real analysis version of integration. I could be wrong, but, at least states-side, most people who take a class called "real analysis" have already taken calculus. –  Thomas Andrews Jun 13 '13 at 15:17
@ThomasAndrews - Yes, that is correct. –  Clarinetist Jun 13 '13 at 15:17
@ThomasAndrews Oh. Where I come from mathematicians don't even take calculus, so I didn't consider that. Maybe the OP can give some more context regarding his situation. Edit: and he already did. –  Git Gud Jun 13 '13 at 15:18
I can go ahead and do that. –  Clarinetist Jun 13 '13 at 15:19
@Clarinetist If you like visual stuff, Visual Complex Analysis by Tristan Needham is very visual. When I read it, I liked to supplement it with a more rigorous text, like Krantz's and/or Ahlfors' Complex Analysis books. –  Ben West Jun 13 '13 at 15:26

## marked as duplicate by Git Gud, Lord_Farin, O.L., Mark Bennet, Peter TaylorJun 13 '13 at 15:56

I'd recommend you look at Gamelin's book Complex Analysis. It is suitable for a good undergraduate who's already had some real analysis.

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This might be helpful. –  Git Gud Jun 13 '13 at 15:23
+1 for this excellent recommendation. Great for self study. –  Mathemagician1234 Dec 10 '13 at 8:12

Should throw my mortarboard into the ring and plug Hilary Priestley's Introduction to Complex Analysis. I'm certainly finding it useful.

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I recommend D.J. Newman & J. Bak's Complex Analysis

It is clear, "short" and contains all the basics on complex analysis. A tthe end of the book you can find some advanced topics like infinite products and special functions.

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