Which Book Is Best for Undergraduate Complex Analysis?

[sutupidmath]

As the title says, I was wondering what would be a good book in Complex Analysis at the Undergraduate Level? I have one or two of them but like neither of them.

 

[sentient 6]

complex analysis by Lars V. Ahlfors seems to be a pretty nice one, to me at least

 

[jtbell]

Moved to the Science Books forum. There might be some other threads here on complex analysis, try a forum search.

 

[lurflurf]

More information on what you are looking for would be good. theory? applications? computations? modern? old fashioned? topology?

Good
Complex Analysis (Graduate Texts in Mathematics) by Serge Lang
-has some extra material -tries to present at two levels which bothers some when they see the stuff at the other level -spends some time exploring before connecting everything up -not every one likes Lang's style.
An introduction to the theory of functions of a complex variable by E. T Copson
classic very good
Visual Complex Analysis by Tristan Needham
good for visualization and conceptual understanding
Elementary Real and Complex Analysis (Dover Books on Mathematics) by Georgi E. Shilov
includes real analysis includes only core material
Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Paul Cartan
highly recommended, but perhaps not as a primary source
A Collection of Problems on Complex Analysis by L. I. Volkovyskii
contains many problems
Theory Of Functions Of A Complex Variable by Andrew Russell Forsyth
classic old fashioned
A Course of Modern Analysis by E. T. Whittaker and G. N. Watson
classic old fashioned

popular average books
Complex Variables and Applications by James Brown and Ruel Churchill
ok applied
Complex Analysis by Lars Ahlfors
just ok crazy expensive short terse
Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B. Conway
Functions of One Complex Variable II (Graduate Texts in Mathematics) (Pt. 2)
weird notation so so

books that seamed good upon very quick inspection. Anyone read them at length?
Theory of Functions of a Complex Variable, Second Edition (3 vol. set) by A. I. Markushevich
Applied Complex Variables (Mathematics Series) by John W. Dettman

 

[sutupidmath]

Wow, great list!

Well I am already in a Complex Variables course, and we are using Complex Variables and Applications by James Brown and Ruel Churchill, which is OK, but has little to no rigor to it. This is what bothers me.

So, what I am looking for is another book that goes somewhat more into the theory...having some topological flavor to it would be a bonus! However, I am not looking for a book that is highly theoretical either and that would take a long time going through it, since I would like to use it as a suplemental source only and be able to keep up with what we are doing in class.

So, which one in the list above is more along these lines?

Thanks a bunch!

 

[clope023]

Schaum's Outlines of Complex Analysis by Murray Spiegel kept me from getting lost in my own complex analysis class.

 

[mathwonk]

my favorites are lang, cartan, from the list above, and also Frederick P Greenleaf's less condensed, and more detailed book.

 

[George Jones]

So, what I am looking for is another book that goes somewhat more into the theory...having some topological flavor to it would be a bonus! However, I am not looking for a book that is highly theoretical either and that would take a long time going through it, since I would like to use it as a suplemental source only and be able to keep up with what we are doing in class.

So, which one in the list above is more along these lines?

Thanks a bunch!

Maybe Visual Complex Analysis by Needham, but I have no experience with the book.

https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20

Use the LOOK INSIDE! feature to look a the table of contents.

 

[fourier jr]

good book in Complex Analysis at the Undergraduate Level?

got to be brown/churchill

 

[qspeechc]

I used Conway Vol. 1 as an undergrad and I think it is a nice book, so I guess I disagree with lurflurf when he/she says it is average. I don't know why anyone would be bothered by unusual notation, because there are almost as many types of notation as there are authors.But then again it is the only complex analysis book I have read. Well, I've read a bit of Needham, but brush up on your school geometry before you read this book.

 

[Sankaku]

Visual Complex Analysis by Tristan Needham
good for visualization and conceptual understanding

This!

It will not follow the same sequence as Brown & Churchill, but you will come back to it again and again for understanding. Although he uses some high-school style geometry (mentioned above), the book really isn't about that. The visualizations of differentiation and contour integrals are brilliant.

Others in that list: I like Shilov's books, but there is nothing in that one that isn't in Churchill. Ahlfors is really the classic text referred to by everyone else, but it is quite short. You may like it - I have only looked at it occasionally. You should be able to find it in every University library in the world.

I quite liked this as a second reference:
Complex Variables by Francis J. Flanigan
https://www.amazon.com/dp/0486613887/?tag=pfamazon01-20

The first half is a review of 2d vector calculus and real harmonic functions, but the second half is really solid. I found the proofs in it much more illuminating than Churchill. It is also an inexpensive Dover reprint.

...you will still go back to Needham for visual insight!

 

[Goldbeetle]

Check out also "Basic Complex Analysis" by Marsden. It's full of exercises.

 

[MathematicalPhysicist]

More information on what you are looking for would be good. theory? applications? computations? modern? old fashioned? topology?

Good
Complex Analysis (Graduate Texts in Mathematics) by Serge Lang
-has some extra material -tries to present at two levels which bothers some when they see the stuff at the other level -spends some time exploring before connecting everything up -not every one likes Lang's style.
An introduction to the theory of functions of a complex variable by E. T Copson
classic very good
Visual Complex Analysis by Tristan Needham
good for visualization and conceptual understanding
Elementary Real and Complex Analysis (Dover Books on Mathematics) by Georgi E. Shilov
includes real analysis includes only core material
Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Paul Cartan
highly recommended, but perhaps not as a primary source
A Collection of Problems on Complex Analysis by L. I. Volkovyskii
contains many problems
Theory Of Functions Of A Complex Variable by Andrew Russell Forsyth
classic old fashioned
A Course of Modern Analysis by E. T. Whittaker and G. N. Watson
classic old fashioned

popular average books
Complex Variables and Applications by James Brown and Ruel Churchill
ok applied
Complex Analysis by Lars Ahlfors
just ok crazy expensive short terse
Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B. Conway
Functions of One Complex Variable II (Graduate Texts in Mathematics) (Pt. 2)
weird notation so so

books that seamed good upon very quick inspection. Anyone read them at length?
Theory of Functions of a Complex Variable, Second Edition (3 vol. set) by A. I. Markushevich
Applied Complex Variables (Mathematics Series) by John W. Dettman

I read Markushevich's textbook, and I plan to continue reading especially now that I have free time after quiting my Msc.