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Visual Complex Analysis

4.38  ·  Rating Details  ·  207 Ratings  ·  13 Reviews
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students t ...more
Paperback, 616 pages
Published February 18th 1999 by Oxford University Press, USA (first published March 27th 1997)
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Sep 29, 2010 Ezra rated it it was amazing
i bought this book for like $76 at borders and i think the clerk thought i was insane (i suspected i was insane.) (clerk: "woah, that's an expensive book. what's it for?" "umm... for fun? i guess...???") buying shit is weird. i know i could get it on for like 18.99 or whatever, but sometimes it just seems too fucked up to do that. i want someone, somewhere, to know that someone found this book browsing in a borders and immediately forked over the cash and walked out with it. things like ...more
Amar Pai
Aug 04, 2014 Amar Pai rated it it was amazing
Really great book... the closest I've come to actually 'getting' complex analysis.

Basic operations like complex multiplication are clearly explained in terms of vector diagrams. Hyperbolic geometry, the Riemann sphere, the winding theorem and other topics really make a lot more sense explained in an intuitive visual manner. Needham created all the illustrations himself using CorelDRAW, LaTex and the complex graphing program f(z) ( They are very nicely done and o
Oct 01, 2010 DJ rated it it was amazing
From a blog post I wrote just after picking this book up:

"Sweet Feynman has it been a fun last couple days! I picked up Tristan Needham’s Visual Complex Analysis from the University of Waterloo library and this book has reminded me why I fell in love with math as a wee lad. The book’s pedagogical approach is to teach math the way mathematicians actually think about it – visually. Needham’s book is chock full of nifty pictures of Riemann spheres, conformal mappings, branches, and more. Complex an
Aug 04, 2011 Yasuhiko rated it it was amazing
This book allows me to think and use complex analysis! Visual image is very useful for human to think.
Dave Eaton
Apr 24, 2008 Dave Eaton rated it it was amazing
It's rare that I would post a book like this as a recommended read. Clearly, it is not one for everybody. But it is, hands-down, the most engaging and delightful mathematics book I have ever encountered.

Needham likens modern mathematics to a hypothetical world where scholars study, discuss, and produce musical scores, but are never willing to play the music. In fact, the playing of music is suspect, somehow beneath the dignity of scholarly music. It doesn't take any effort to see how tragic this
Nishant Pappireddi
Aug 22, 2014 Nishant Pappireddi rated it it was amazing
I got this book because I was promised geometrically intuitive explanations of the results in a standard Complex Analysis course, and I was not disappointed! Almost every result the author stated was "proved" with a readily understandable geometric argument, which gave me a lot of intuition about why the results are true. Of course, the proofs were not rigorous, but that's what a Complex Analysis class is for.

Many other people have said that one should read this book only after completing a Comp
Zack Garza
Sep 04, 2015 Zack Garza rated it it was amazing
Comes at the task of defining calculus on complex functions from a primarily geometric viewpoint, which makes things intuitive and easy to follow.

Very approachable, even coming from an undergraduate background, although a bit of exposure to real analysis beforehand would definitely help elucidate some of the arguments.

Only downside - the figures can be a convoluted at times, and are often a page or two away from their respective descriptions or explanations. Needham also occasionally fails to m
Feb 01, 2016 Coleoid rated it really liked it
This is a fantastic book on complex analysis, especially if you're more of a visual learner like I am. I highly recommend this to anyone interested in complex analysis, whether you'll be actively reading it or keeping it as a reference. Pair this with a book on the applications of complex variables to get the most out of it.
Ronald Lett
May 12, 2011 Ronald Lett rated it it was amazing
Shelves: analysis
A beautiful exposition of the geometry behind complex analysis and topology! Assuming you have already been exposed to complex calculus, the great connections made in this text with modern geometry, topology and algebra will solidify your work with complex numbers as a geometrical language.
Feb 12, 2011 zltg rated it it was amazing
Shelves: math
This book is amazingly well written. The presentation is beautiful. The ideas are well presented and easy to understand, but nontrivial and deep. I cannot imagine how an introductory book on complex analysis can be better written. I'll have to read it again sometime.
Jul 16, 2012 Edwin rated it it was amazing
This book is a gem. If you want a feel for complex analysis and want to experience the motivation behind some fuzzy concepts that are introduced in terse texts, then this book is for you. This book will show you the beauty that is complex analysis.
Mauricio Eguez
Nov 25, 2008 Mauricio Eguez rated it really liked it
Great way to approach complex analysis. I am not reading this book linearly, but rather using it to enhance my knowledge of complex analysis. A standard text in complex analysis is a good complement.
Jun 17, 2007 Robert rated it really liked it
This is the way ACM 95a should be taught.
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