Visual Complex Analysis: 25th Anniversary Edition
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FROM THE AUTHOR:
All legitimate copies of VCA produced by Oxford University Press are crisply printed on high-quality paper. If you obtain a shoddily printed copy, it’s a fake: please return it and purchase a genuine OUP copy.
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The fundamental advance in the new 25th Anniversary Edition is that the original 501 diagrams now include brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way―as a highbrow comic book!
The 25th Anniversary Edition also features a new Foreword by Sir Roger Penrose, as well as a new Preface by the author.
Complex Analysis is the powerful fusion of the complex numbers (involving the ‘imaginary’ square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years.
This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality.
REVIEWS FROM THE BACK COVER:
“I was delighted when I came across Visual Complex Analysis. As soon as I thumbed through it, I realized that this was the book I was looking for ten years ago.”
Ed Catmull, former president of Pixar and Disney Animation Studios
“Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis.”
Sir Roger Penrose
“If your budget limits you to only buying one mathematics book in a year then make sure that this is the one that you buy.”
Mathematical Gazette
“. . . it is comparable with Feynman’s Lectures on Physics. At every point it asks “why” and finds a beautiful visual answer.”
Newsletter of the European Mathematical Society
“. . . an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas from a geometric point of view. The style is lucid, informal, reader-friendly, and rich with helpful images (e.g., the complex derivative as an “amplitwist”). A truly unusual and notably creative look at a classical subject. ”
Paul Zorn, American Mathematical Monthly
“Newton would have approved . . . a fascinating and refreshing look at a familiar subject . . . essential reading for anybody with any interest at all in this absorbing area of mathematics. ”
Times Higher Education Supplement
“It is . . . a special pleasure to see Tristan Needham’s Visual Complex Analysis with its elegantly illustrated visual approach.”
Ian Stewart, New Scientist
“The new ideas and exercises bring together a body of information potentially invaluable to researchers in fields from topology to number theory . . . this is only the beginning of a long list of famous facts for which Needham offers attractive visual proofs . . . Cauchy’s theorem is a satisfying example: you can see the contribution to the integral from each infinitesimal square vanish before your eyes.”
Frank Farris, American Mathematical Monthly
“The arguments constructed are highly innovative; even veterans of the field will find new ideas here. . . .This is a special book. Tristan Needham has not only completely rethought a classical field of mathematics but has presented it in a clear and compelling way. Visual Complex Analysis is worthy of the accolades it has received.”
MAA Reviews
9 reviews for Visual Complex Analysis: 25th Anniversary Edition
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mitchus k. –
This is a great book for getting visual intuitions for the universe of complex numbers. The 25th anniversary edition has been refreshed with new content and improvements all around. Can heartily recommend
Jean M. Gawron –
Quite simply, I love this book. I came to it by way of Roger Penrose’s Road to Reality, which says some very flattering things about Needham, and being a fan of Penrose’s book, I tried out Needham’s. If you loved Road to Reality, and learned something from it, there is a good chance you will also love Visual Complex Analysis. Having said that, they are not the same kind of book. Penrose has an end in mind, and the book arcs toward it, supplying you at each step with what you need to take the next. Needham’s book is a leisurely tour through a particularly beautiful part of the landscape of math. You are there for the views, to stand lingering at the precipice watching the sun set. If you an engineering or physics student interested in complex analysis because you need to get on with your physics and engineering work, this book is not for you. Complex Differentiation and the Cauchy-Riemann equations are not introduced until Chapter 4. There is way more time spent on topics like the Riemann sphere and Mobius transformations than any reasonable textbook could afford. There are extended discussions of individual functions on the complex plane, like the exponential function, the log function, the trigonometric functions. Why? Because they are beautiful. Because these are all places where there is an exploision of hidden structure in the complex plane. Needham has a gift for revisiting elementary topics and bringing out their beauty. The discussion (and proof?) of Euler’s Equation is inspiring. All this is very untextbooklike. Also untextbooklike: there are few exercises, and they are not really designed to work the reader through a minimal skill set. Like the rest of the book, they focus on the areas where the views are good. Readers turning to complex analysis for practical reasons are better off with Gamelin. But if you want insight, and a fresh look at old ideas, and the occasional flash of purely geometric intuition, then this book is for you. Or if you too believe that the complex plane is the doorway to some beautiful mathematics, then this book is especially for you.
VIDAL Diego –
Testo che punta più sugli effetti speciali grafici (che non sono, comunque, eccezionali) che sulla teoria delle funzioni analitiche. Infatti, a parte il teorema di Cauchy, mancano Picard, Rouchè & company.
DaveM –
The graphics are phenomenal and insightful.
Pierre Bulens –
J’avais déjà la première édition de cet excellent ouvrage que je recommande à tous ceux qui connaissent ou veulent apprendre l’analyse complexe. Une façon tout à fait différente d’aborder cette matière. Une autre façon est développée dans un autre ouvrage remarquable : Applied and Computational Complex Analysis de Peter Henrici (3 tomes).
J’ai offert cette édition du 25ème anniversaire à mon fils, et je l’ai achetée pour moi. Un régal de s’y replonger.
JUERGEN MUELLER –
Laut Autor dauert das Durcharbeiten 1 Jahr…….
Riccardo –
Tristan Needham da qui il suo meglio. Un libro che può essere considerato di testo, tuttavia è molto di più poiché apre nuovi orizzonti su quanto si sa sui numeri complessi.
Una lettura da consigliare a chiunque si applichi in modo non banale sia in fisica che in matematica.
Un capolavoro nel suo genere.
Alvaro –
If you want to understand Complex numbers, this is your books. Maybe the proofs could be more rigorous, but you can find toons of proofs in other books which you will be able to understand thanks to the explanations in this one.
Mario Lemelin –
I liked the fact that there are numerous figures, Amplitwist (antiderivative), Mobius transformation and non-euclidean geometry.