Recommend textbook for complex analysis

[micomaco86572]

Could someone recommend an accessible and well-known textbook of complex analysis for graduate education? thx

 

[HallsofIvy]

I've always liked "An Invitation to Complex Analysis" by Ralph Boas.

 

[micomaco86572]

I've always liked "An Invitation to Complex Analysis" by Ralph Boas.

Thx!

 

[micomaco86572]

Does someone know something about Complex Variables: Introduction and Applications by Ablowitz? This book is highly rated in Amazon.
Is it accessible? Is it too mathematical?

 

[AxiomOfChoice]

Another book that comes very highly recommended on Amazon is "Visual Complex Analysis" by Needham: https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20

But my favorite complex analysis text - the one I've found most informative, accessible, and readable - is the one by Stein and Shakarchi: https://www.amazon.com/dp/0691113858/?tag=pfamazon01-20

In my graduate course, we used Gamelin's book, which is ENCYCLOPEDIC in scope. But some of his proofs seem to be a little sloppy and take a lot for granted: https://www.amazon.com/dp/0387950699/?tag=pfamazon01-20

The canonical graduate text - for YEARS - has been Ahlfors: https://www.amazon.com/dp/0070006571/?tag=pfamazon01-20. But for some reason, it costs $200!

 

[Anthony]

Does someone know something about Complex Variables: Introduction and Applications by Ablowitz? This book is highly rated in Amazon.
Is it accessible? Is it too mathematical?

The book by Ablowitz and Fokas is very accessible and reaches a wide range of topics. :)

 

[Zorba]

Ahlfors is a graduate text? I don't know about that really, it serves me fine as an undergraduate text, very well written, I would recommend it.

I have heard people raving like crackpots about how amazing Needham's book is, so I would recommend that also, been meaning to get my hands on that now for a while.

If I may be so bold to ask, can anyone recommend one with lots of exercises.

 

[micomaco86572]

thank you all, U did me a big favor!

 

[AxiomOfChoice]

If I may be so bold to ask, can anyone recommend one with lots of exercises.

There is always the option of purchasing Serge Lang's book and the detailed solutions manual, written by Shakarchi.

Lang: https://www.amazon.com/dp/3540780599/?tag=pfamazon01-20

Shakarchi: https://www.amazon.com/dp/0387988319/?tag=pfamazon01-20

 

[Landau]

Bruce Palka also wrote a nice book, in the UTM series: click.

 

[profanilp]

The classic of alfhors is excellent but terse.
the conway book is boring. It introduces analytic functions as continuously differentiable functions and messes up simple integration . it has messed up a simple problem of integrating multivalued function by avoiding the use of branches.a very wrong text.
lang's is good . emphasis on poewer series is good but formal ower series is unnecessary.
pristley is good but treatment of cauchy's theorem is not satisfactory. it is good at conway but not initial version . churchill is good but gain general treatment of cauchy's theorm is not there.
lanfg and alfhors both use interhange of order of integration. rudin is too te5se and does not mention laurent's theorem! a great lacuna!
my notes partly on wikipedia partly on my website and partly with my students have avoided all drawbacks. we have complete homology vversion of cauchy theorem but do not need homotopy version formaly. also we have original treatment of elementary fnctions