Calculus of complex numbers textbook?

[Heretic Apostate]

I have a B.S. in applied mathematics. That means, while I like math, I'm not good at the theoretical stuff. But I want to be. Sure, it's been 12 years since I've taken a challenging math class (that's not bragging; what I mean is, I graduated 12 years ago), but I still wince every time I think back to my experiences with calculus of complex numbers.

I'm hoping there are serious math junkies on here, who can point me to a textbook that someone who is an average math major (i.e., top 2% of the nation, which is definitely average for a math major ) can understand. I am getting back into math, after a long, long, LONG hiatus, and I want to conquer this class, as well as other classes I couldn't figure out when I was in college.

A little help here?

Thanks!

 

[The Axe]

Hey!

For an introductory book, you might try Complex Variables with Applications by Churchill/Brown; that's the book we use for our graduate class (that I don't get to teach---#@$%!). Also highly thought of is Classical Complex Analysis by Hahn/Epstien. You might like Fundamentals of Complex Analysis for Mathematics, Science, and Engineering by Saff/Snider better given that you have an applied bent.

My first CA course was from Complex Analysis by John Conway; it's pretty theoretical (mainly just theorem/proof with a few examples thrown in), but does a good job of covering most of the basics. If you're in the need for some humbling, there's always Complex Analysis by Lars Ahlfors---that's about as thorough a treatement as you can get.

 

[Umbran]

I can seccond the suggesation of Complex Variables with Applications by Churchill/Brown. Most of my complex calculus came by way of physics courses, but the above text was very useful.

 

[Heretic Apostate]

I can't find Churchill/Brown. Do either of y'all have an ISBN?

 

[The Axe]

Actually, now that I think about it, they may have reversed it to Brown/Churchill in the current edition.

Google say ISBN: 0070109052

 

[Brennin Magalus]

My first suggestion is also Churchill and Brown (you can get an international softcover for around $40). Other suggestions are Marsden and Hoffman (more abstract), Saff and Snider, and Wunsch.

 

[Heretic Apostate]

Wow...

I subscribe to the Scientific American magazine. Lately, the Scientific American book club has been advertising six books as an introductory offer (The Joy of Pi, Infinity and Beyond, etc.). Not wanting to get roped into a book club deal, I bought the books on Amazon.

I'm working my way through the history of sqrt(-1). ("An Imaginary Tale") All I can say is, I think I have to start again in my Calc 1 textbook, because I don't think I'm anywhere near ready for the stuff in the complex analysis books.

Luckily, I'm a packrat, and I've still got my Calc 1 book, as well as my Calc 2-4 book, plus four books of mathematical equations and tables (like I said, I'm a packrat, and I love library book sales...). I've just received the first of four complex analysis books I've ordered, and I think I'll crack it open this week to give it a try.

But I'm sure as heck glad I went into accounting rather than theoretical math or electrical engineering.

 

[The Axe]

I'm working my way through the history of sqrt(-1). ("An Imaginary Tale") All I can say is, I think I have to start again in my Calc 1 textbook, because I don't think I'm anywhere near ready for the stuff in the complex analysis books.

As nasty as the history of that stuff looks, mathematicians have done a lot to make most of that stuff much easier. Early mathematicians who made advances were geniuses (geniui?) because they had to be: they didn't have the spiffy notation/techniques that let us mere mortals to do stuff in modern days.

 

[der_kluge]

Why can't you just spend your time working on Fermat's last theorem? Isn't that complex enough?

 

[Heretic Apostate]

Why can't you just spend your time working on Fermat's last theorem? Isn't that complex enough?

I've got a truly elegant solution to Fermat's last theorem, but I don't have space here to write down the proof.

(edit: I misremembered the story about Fermat, changed my answer to more suitably paraphrase him)