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Visual Complex Analysis

4.44  ·  Rating details ·  422 ratings  ·  23 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 Clarendon Press (first published March 27th 1997)
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Average rating 4.44  · 
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Jan 02, 2009 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
May 28, 2010 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
Amar Pai
Aug 16, 2010 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
Mar 23, 2016 rated it really liked it
Shelves: matematica
Found on Penrose's "Road to Reality" Bibliography.
I needed this book as a primer to non-euclidian geometry and complex integration.
Above all, you'll love how it feels when the author really wants that you really understand a so advanced topic.
Kaung Thu
Jun 01, 2019 rated it it was amazing
As someone who was introduced to the complex analysis by this book, I highly recommend this book even for a beginner (You need to have some grasp on Calculus but I assume everyone who is trying to touch this whole topic would have done this prerequisite.) The illustrations, explanations, and examples all go in an excellent presentation style. You can ignore the exercise to understand the fundamental concepts. But when u do, make sure to give time to have a deep overall understanding. (Sometimes ...more
Dave Eaton
Apr 24, 2008 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
Jun 23, 2014 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
Ronald Lett
May 12, 2011 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.
Aug 04, 2011 rated it it was amazing
This book allows me to think and use complex analysis! Visual image is very useful for human to think.
Tom Schulte
May 18, 2020 rated it really liked it
This is an engaging and clear introduction to complex analysis with a focus on visual display and easily followed consideration of translations, rotations, scaling and similar transformations of shape, orientation, and location. This is not an introductory text, so the author recommends reading first or having on hand Complex Analysis. I think this itself goes nicely with Spherical Geometry and Its Applications. ...more
Bob Woodley
Jan 01, 2019 rated it it was amazing
A visual introduction to one of the most beautiful parts of mathematics: complex analysis. Written before the glory days of computer graphics, which mean the author had to come up with meaningful diagrams and schematics.

Such insights. This book had a huge influence on my work for 2 years following reading it.

And I still have a chapter or 2 to go. Who knows when I'll get back to it.
Julius Zhang
Aug 11, 2018 rated it it was amazing
This is the most enjoyable maths textbook that I have read.

The texts provided with the numerous illustrations offer an easy, intuitive introduction to complex analysis. With that said, most theorems in a first year complex analysis course are covered and I found it really helpful to follow up with a more traditional textbook on the details of the proofs.
Jan 01, 2016 rated it it was amazing
"The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity. " ~ Leibniz

As a undergraduate calculus student who hasn't taken his first contour integral, I must admit that I bit off more than I can chew with this book. That said if you aren't in over your head, how will you ever know how tall you are? As I approached the boundaries of my current knowledge with
Zack Garza
Jan 22, 2015 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
Oct 24, 2015 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.
Jul 16, 2012 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.
Feb 12, 2011 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.
Mauricio Eguez
Nov 25, 2008 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 rated it really liked it
This is the way ACM 95a should be taught.
Adam Lantos
Aug 23, 2018 rated it it was amazing
A book whose purpose is to provide the reader with much needed intuition for complex analysis through visual representations of the material. It's the best supplement for any complex analysis books out there because it is mostly useful in understanding what the hell you are actually learning/doing. The only proofs here are the ones that are not lengthy and contribute to the understanding. This book is a gem for everybody who wants to build some intuition on complex analysis but it should not be ...more
Oct 08, 2020 rated it it was amazing
This is a great and gentle guide to complex analysis. The informal writing, story-telling approach to mathematics hints that this book is aimed towards undergraduate students, distinguishing itself from dry and rigorous arguments in standard textbooks. I enjoyed studying this book and it certainly helped me understand what I sought to learn. However, in order to read this book fluently and to truly appreciate Needham's vivid presentation of the subject matter, one should already possess some pri ...more
Aug 23, 2020 rated it liked it
Useful as a supplement for a rigorous course on complex analysis.
Not a good stand-alone book!
Jul 25, 2020 rated it it was amazing
amazing book you don't even need to be professional maths man
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Sep 30, 2012
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Andy Williamson
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Jun 01, 2014
Kshitij Tyagi
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Dec 05, 2013
Bir Kumar
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Oct 10, 2016
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Mar 21, 2019
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Prerequisites please! 2 20 Mar 05, 2017 11:31AM  

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