Visual Complex Analysis

Tristan Needham

Oxford University Press

[VCA cover illustration]

"I can only describe this book as amazing... it is not an exaggeration to say that there are gems in every section ... even familiar facts are frequently explained in refreshingly new ways in this wonderful book. ... many of these exercises are so absorbingly interesting that it is difficult to leave them alone. ... If your budget limits you to buying only one mathematics book in a year then make sure that this is the one that you buy."

"The pictures in this note were produced directly in PostScript. ... There are other possibilities—one very fine recent example of mathematical graphics at a high level is Needham’s Visual Complex Analysis, which used quite different tools."
Bill Casselman, NOTICES OF THE AMS

"Too many textbooks neglect the historical foundations; this book is rich with history. The author has taken full advantage of modern computer graphics to provide a variety of lovely and helpful pictures... There is a rich bibliography at the end of the book spanning the gamut of both historical and modern references."

"For the more mathematically inclined who also have an interest in keeping one foot in physical reality, I highly recommend Tristan Needham, Visual Complex Analysis"
An Imaginary Tale, Princeton Univ. Press, 1998
by Paul Nahin

"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, OM

"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, President of Pixar Animation Studios and Walt Disney Animation Studios

Click here to listen to Douglas Hofstadter (author of the Pulitzer Prize-winning bestseller "Godel, Escher, Bach") discussing Visual Complex Analysis.
Douglas Hofstadter, interviewed by

"Newton would have approved. ...a fascinating and refreshing look at a familiar subject. ... It is essential reading for anybody with any interest at all in this absorbing area of mathematics."

" is comparable with Feynman's lectures in Physics. At every point it asks 'why' and finds a beautiful visual answer. ...I believe that this book can make every student understand and enjoy complex analysis. If its methods could be applied in teaching more generally, mathematics would become a flourishing subject"

"... 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."

"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. ... to replace our rich visual intuition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices—but his are interesting."

"This informal style is excellently judged and works extremely well...Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in some field where complex analysis is used."

In addition to the reviews quoted above, the June-July 1998 issue [Vol. 105, No. 6] of the American Mathematical Monthly contains a seven page review by Prof. Frank Farris.

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. Although aimed at the complete beginner, professional mathematicians and physicists may also enjoy the fresh insights afforded by this unusual approach. The book contains:

Much of the work grew out of a study of Newton's Principia, and Subrahmanyan Chandrasekhar was able to use some of the ideas and illustrations in his Newton's Principia for the Common Reader.

Tristan Needham is a Professor of Mathematics at the University of San Francisco. For part of the work in this book the Mathematical Association of America presented him with the Carl B. Allendoerfer Award.

In October 1997 Visual Complex Analysis received First Prize in the National Jesuit Book Award Contest for Mathematics/Computer Science books published in 1994, 1995, 1996.

PDF Extracts:

[PDF icon] Preface [PDF icon] Mathematics

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Contents Preface
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Translations: German (2001), Japanese (2002), Chinese (2009)
Hardback Errata
(updated 22-7-98)
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30th June, 2011