Books on complex analysis
in [Math]
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From: David C. Ullrich on 7 Jul 2010 12:08 On Wed, 07 Jul 2010 10:11:14 -0500, Stephen Montgomery-Smith <stephen(a)math.missouri.edu> wrote: >Edson wrote: > >> Anyway, my present goal is to study complex analysis, something fascinating. I've been introduced to complex numbers, I know they form a field with respect to addition and multiplications. I've grown out of that phase when i = sqrt(-1) seems something mystical. So, I'd like some opinions on books on complex analysis for someone at my level. > >I have heard high praise about the book "Applied Complex Analysis with >Partial Differential Equations" by Nakhle H. Asmar. It is at the >undergraduate rather than graduate level. And I should add that Nakhle >is a good friend of mine. heh-heh. That's totally unacceptable here on sci.math, suggesting a book written by someone you know. >But I really do hear a lot of unbiased praise >for this book from students.
From: Han de Bruijn on 8 Jul 2010 03:01 On Jul 7, 4:41 pm, Edson <edson...(a)yahoo.com> wrote: > > Hi > > > I'm somewhat young (15) but I have studied some math. > > I started at number theory, but then I was introduced > > to analysis and found it very interesting. And I know > > it's very important in several practical fields like > > engineering, economics and optimization. > > > I've been studying it for almost 2 years, in Rudin's > > and Bartle books. I've also studied some analysis in > > R^n. I consider to become a mathematician, though > > many people keep telling me to graduate in something > > else. > > > Anyway, my present goal is to study complex analysis, > > something fascinating. I've been introduced to > > complex numbers, I know they form a field with > > respect to addition and multiplications. I've grown > > out of that phase when i = sqrt(-1) seems something > > mystical. So, I'd like some opinions on books on > > complex analysis for someone at my level. > > > I've had the opportunity to browse through 2 best > > sellers. One of them is the classic Alhfors' Complex > > Analyis, the other (a moderm book, launched about 2 > > years ago, still in its 1st edition) is Ulrich's > > Complex Made Simple (so he claims!). I could read the > > first chapters of each book. Well, exaggerating a > > bit, to me they seem books on different subjects, the > > approaches are quite different. If I had to decide > > right now, I'd get Ulrichs's book. At least to me, it > > looks, say, more reader friendly, easier to > > understand. I could understand why the integral of a > > holomorphic function along a closed smooth curve is > > zero, though I couldn't get sure if the set where the > > curve lies must be convex or just connected (or > > simply path connected). > > > Alhfors is very clear in the first 2 chapters, but > > somewhat complicated when he introduces derivatives > > and integrals. I couldn't understand why every > > differentiable function is infinitely diferentiable. > > I think in Ulrich's book this is clearer and easier > > to understand. But I got somewhat shocked with the > > two completely different approaches. > > > I'd like to mention 2 other points: > > > 1. The proofs that power series can be differentiated > > term by term are completely different. Ulrich's > > proof, maybe original, is kinda cool, although he > > implicitly assumes the reader knows something about > > functions from C^2 to C (but, after all, the concepts > > involved are the same as those of functions from R^2 > > to R). > > > 2. In Alhfors book, the proof of the Cauchy Riemann > > equations are very easy (actually, I did it myself > > before reading the proof. I'm not boasting, it's not > > t big deal, anyone who has studied limits can do it. > > All you have to know is the limit is the same no > > matter how you approach the point). But Ulrich's > > approach, though not so intuitive, is great, the > > reader sees the link between complex > > differentiability and differentiability in R^2. > > Really cool! > > > I'd like some help on this. What book should I > > choose? Actually, I have a 10-year-old edition of > > Alhfors book, my father was a mathematician (although > > he was a number theorist, he studied much analysis, > > including complex analysis, and even taught Calculus. > > Once I heard him say to some students that the zeta > > function had much to do with prime numbers. Then, I > > had no idea what the zeta function was. Now, I'm > > dying to know what that series has to do with prime > > numbers). My father can't help me any more, but if > > someone here can, I'll be grateful. > > > Edson > > > (Maybe Dr. David Ulrich himself. I know he > > contributes to this forum) > > Thank you all for your help. > > And I bought Complex Made Simple! Hope I can follow it! > Edson I've read the first few chapters of it and then gave up, due to lack of whatever (time, motivation, intelligence, discipline). It certainly has been worth buying, though. Here are some (2009) comments of mine: http://hdebruijn.soo.dto.tudelft.nl/jaar2009/CMS.htm Han de Bruijn
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