Reference book for complex analysis.

Question

I have a complex analysis test in 15 days. I have never studied the subject before. The only analysis I know is the first 7 chapters of baby Rudin. I plan to learn some multi-variable analysis and then start complex analysis. I have Rudin's Real and Complex Analysis and Complex Analysis by Lars Ahlfors, but they seem like books that would take a lot of time to study. I'm looking for a book with really simple proofs, yet ones which cover a decent bit of ground. The easiest book I have read so for is Real Analysis by Robert Bartle. Can someone suggest a book for complex analysis which is as easy as Bartle? Thanks.

Complex analysis is a fairly large subject. Can you be a bit more specific? — Chappers, Apr 14 '17 at 13:45
The topics I have for my test are analytic functions, cauchy's theorum, cauchy's integral formula, max modulus principle , laurent series, singularities, theory of residues, contour integration, — tony, Apr 14 '17 at 13:48
Not sure if you can do it in 15 days, but Basic Complex Analysis by Marsden&Hoffman is a good book for beginners, it's straightforward and gets into complex line integrals & Cauchy's integral theorem in just the second chapter. I wouldn't recommend rushing complex analysis, but if you just want to pass the test you're good with that i think. — Arbiter, Apr 14 '17 at 13:49
@Dimitris, I will check it out. Would what I learnt in rudin be enough as prerequisites? — tony, Apr 14 '17 at 13:50
@tony, I haven't read baby rudin (that's principles of analysis one right?). I'd say you need some basic understanding of real analysis and multi-variable functions, plus double and line integrals (baby rudin doesn't have multiple integrals right?). — Arbiter, Apr 14 '17 at 13:57
Understanding the Riemann integral definition is the basic idea, if you understand that you'll understand the rest double,line etc, comlpex integrals too. — Arbiter, Apr 14 '17 at 14:01
@ThomasAndrews, im doing self study. Preparing for enterance exam. — tony, Apr 14 '17 at 14:03
@tony, good luck, you can always start reading (mardsen or whichever you chose) if you feel confident and have rudin or any good analysis book on your side to help with whatever you don't understand. — Arbiter, Apr 14 '17 at 14:07
I recommend getting a copy (there might be one in your University's library) of the Schaum's Outline of Complex Variables. — Dave L. Renfro, Apr 14 '17 at 15:42
@DaveL.Renfro, I will check it out. But does this book discuss complex analysis in the pure math aspect? or is it a book for engineers and physics students? — tony, Apr 14 '17 at 16:09
The book can serve both, which makes it a bit theoretical for engineers and not quite up to the Ahlfors and Conway level that you'd want for a solid graduate level treatment. However, given the amount of time you have available, I think it will work much better than a typical textbook. Also, a lot of what you'll probably be asked won't be about detailed proofs of big theorems (e.g. identity theorem for analytic functions), but rather what they say and what are some reasonably easy consequences of them, and the Schaum's book does have a lot of that. — Dave L. Renfro, Apr 14 '17 at 16:41

score 1 · Accepted Answer · answered Apr 14 '17 at 13:57

When I took the course a few years ago, the notes of Ash and Novinger were recommended to me as they are designed to be gone over in a compressed time period. So they might be a good thing to look at. They are available online at:

http://www.math.uiuc.edu/~r-ash/CV.html

Then use Rudin and Ahlfors for additional exercises. There are many solution manuals to Rudin available online, and many of the problems are discussed on Stack Exchange if you look for them.

Best,

--Kris

Reference book for complex analysis.

1 Answers1