Introduction to Complex Analysis

[josephcollins]

Hi people,
I'm Joseph, 17, English studying European Baccalaureate. I was wondering if anyone here could recommend for me a good introductory book on Complex Analysis that requires only an understanding of the complex numbers you would cover in High School Maths. Maybe something that is ideal for undergraduates?, I've covered Complex Numbers at school this year and look forward to studying them in more detail at University, just want to look at complex numbers in a bit more depth now, does anyone know anything good? I'd be most grateful for a good suggestion.
Thanks

 

[arildno]

I like Bak&Newman's "Complex Analysis"

 

[JohnDubYa]

The Schaum's outline series book (from McGraw-Hill) is excellent.

Churchill is good if you want physical applications. For more advanced discussion I suggest Palka.

 

[sambo]

Personally, I found Churchill to be a bit tedious (sorry, just my opinion). I found "Complex Analysis" by Lang to be very good--especially if you take the time to do the excercises. It get's to the point of WAY beyond high school, but it builds slowly, and you can always stop once you hit the wall.

 

[quantumdude]

Personally, I found Churchill to be a bit tedious (sorry, just my opinion).

Is that Churchill and Brown? I didn't care for that either. If it weren't for the Schaum's Outline, Complex Variables, I'd have had a much more miserable time in that course.

 

[geometer]

Another good book, although maybe a little advanced is "Complex Variables with Applications," by David Wunsch. Published by Addison-Wesley Publishing Company.

 

[HallsofIvy]

"An invitation to Complex Analysis" by Ralph Boas is an excellent introduction.

 

[fourier jr]

You guys didn't like the Brown & Churchill book? I thought that was great. I never used Bak & Newman's one, but I've looked at it & I think that's good too.

 

[JohnDubYa]

I forgot all about Boas. Definitely a good suggestion.

 

[fourier jr]

Just for fun I had a look at Bak/Newman's book today, and I would say that it's got tons of useful, cool stuff in it. I would also say that it isn't a real good intro to complex variables because it has a bunch of topological concepts like compactness, convexity, etc etc. The book that the physics students use at my school is the one by Brown/Churchill, which I have & I would say it's the best one with no topology in it. Schaum's is always good too, and usually much cheaper than other books to boot. The only cheaper math books are put out by Dover as far as I know.

 

[mathwonk]

I would suggest that sometime it is a healthy idea to learn about compactness and convexity.

The difference between compactness and non compactness is like the tension between a bounded or an un - bounded universe in physics. I.e. a set is compact if an infinite collection of points must always bunch up somewhere.

mathematically compactness is a generalization of the notion of finiteness, which is pretty basic.

convexity is of course as fundamental as the difference between an ellipse and a hyperbola, which is relevant to reflected sound waves, light, etc.

 

[mathwonk]

the nice thing about complex analysis books is they are all good, (so buy a cheap one), but probably only a mathematician can love Ahlfors' classic text, which has inadequately brief problem sets.

some wonderful cheap books are the classic "elementary theory of analytic functions of one or several complex variables" now in paperback by henri cartan, $11.95, and the book "Analytic Function theory" by Einar Hille, for $14.95 (vol 1). Vol 2 of Hille is also outstanding but may be out of print.

 

[eJavier]

I think you should be familiar with at least some Calculus before trying to get into Complex Analysis. I don't know if you are by the way, I ain't familiar with european education