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Visual Complex Analysis Paperback – February 18, 1999

ISBN-13: 978-0198534464 ISBN-10: 0198534469 Edition: n

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Editorial Reviews


"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." --Roger Penrose

"Tristan Needham's Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing us attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses. I am tempted to hide the book from my own students, in order to appear more clever for popping up with crisp historical anecdotes, great exercises, and pictures that explain things like that mysterious 2*pi that crops up in integrals. Whether you use Visual Complex Analysis as a text, a resource, or entertaining summer reading, I highly recommend it for your bookshelf."--American Mathematical Monthly

"Delivers what its title promises, and more: an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas. . .A truly unusual and notably creative look at a classical subject." --American Mathematical Monthly

"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But 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." --New Scientist

"Committed to the exclusive use of geometrical arguments and content to pay the price of 'an initial lack of rigour', he has produced a radically new text. The author writes "as though [he] were explaining the ideas directly to a friend". This informal style is excellently judged and works extremely well."--Mathematical Review

"This is a book in which the author has been willing to make himself available as our teacher. His own voice enters in a rather charming way....I recommend Visual Complex Analysis, as something to read and enjoy, to share with students, and perhaps to inspire other books in which the voice of the author is vividly present to teach and explain."--American Mathematical Monthly

From the Author

The book recently won First Prize in the National Jesuit Book Award Contest for the best mathematics or computer science book published in 1994, 1995, or 1996. --This text refers to an out of print or unavailable edition of this title.

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Product Details

  • Paperback: 616 pages
  • Publisher: Oxford University Press; n edition (February 18, 1999)
  • Language: English
  • ISBN-10: 0198534469
  • ISBN-13: 978-0198534464
  • Product Dimensions: 9 x 1.3 x 6.1 inches
  • Shipping Weight: 1.9 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (62 customer reviews)
  • Amazon Best Sellers Rank: #194,928 in Books (See Top 100 in Books)

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Customer Reviews

This book is among the best math books one will ever find!
Paul J. Papanek
This is a great book for a Complex analysis course, especially when combined with a more traditional text like Ahlfors or Knopp's Theory of Functions.
Walter Jacob, IV
This book can therefore be an ideal way to get started with complex analysis or even to further one's understanding in the subject.

Most Helpful Customer Reviews

142 of 144 people found the following review helpful By mzb on November 13, 2001
Format: Paperback
Needham's book is a masterpiece which will be appreciated by anyone who already has gained (or is simultaneously gaining) a firm knowledge of the traditional, i.e. more algebraic, approach to complex analysis. In addition to reading it for pleasure, I have used the book extensively in teaching 18.04 Complex Variables with Applications at MIT, not as a required textbook, but rather as inspiration for lectures and homework problems. The book helps me give the students (mostly undergraduates in applied mathematics, science, and engineering) the geometrical insights needed for a deeper understanding of the subject, beyond what is found in various standard texts, such as Churchill and Brown or Saff and Snider (the required textbook for 18.04). As a prelude or companion to Needham's book, however, I would recommend reading one of these other books and working through more straightforward examples of algebra and calculus with complex functions. With that said, Needham's book is a perfect supplement to a first course in complex analysis.
Needham's book is unique in its clear explanation of how the rich properties of analytic functions all follow from the "ampli-twist" concept of complex differentiation. In my class, I use this crucial, geometrical idea from the first mention of the derivative, where it goes hand in hand with the concept of conformal mapping (which is often at the back of introductory texts, but which I think should appear near the beginning). Perhaps the most delighful section of Needham's book is the one where he uses the same ampli-twist concept to give a very intuitive, unified proof of Cauchy's theorem, Morera's theorem, and the fact that a loop integral of the conjugate gives 2i times the area enclosed.
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81 of 83 people found the following review helpful By Paul J. Papanek on January 9, 2004
Format: Paperback
What a great book this is!
This is a book that any math afficionado must have, and will undoubtedly savor. I frankly don't understand those reviewers who have given this book fewer than five stars. In fact, five stars wouldn't seem to be enough here. This book is among the best math books one will ever find! What else would one want from a such book? It is exciting, friendly, creative, often funny, crystal clear, fresh, deep, and unfailingly courteous to the reader--a quality not always found in math texts.
Additionally, this book succeeds on another level -- it is just plain beautiful. Math, to be great, must be beautiful, while books about great math too often are not. This book is truly beautiful, even artful. The author has taken great care to create beauty here.
I intially bought this book, because as an ex-mathematician whose analysis skills were getting rusty I wanted to revisit complex analysis. This book certainly succeeded in brushing up those old skills, but it also deepened them. The book has marvelous insights and geometric drawings that demonstrate in a clever way the links between complex analysis and other branches of math and physics. How could one not love the lovely and intricate drawings that depict, say, loxodromic transformations on a sphere, or the eye-popping diagrams of rotations in hyperbolic space? They're fabulous! Even the problem sets are delightful.
As a side note, some of the historical glosses about mathematicians are also very lively, and are another source of pleasure here.
On the dust jacket is the blurb--"If you must buy only one math book this year, this is the one to buy." I have to agree. I bought a couple dozen math books last year, and this one outshines the rest. I can't recommend it highly enough, even if you already feel comfortable with complex analysis.
I encourage my fellow readers to pick this up, and see how beautiful a math book can be.
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25 of 25 people found the following review helpful By Shankar N. Swamy on August 18, 2000
Format: Paperback
This book attracted my interest mainly because of its geometry content, and sustained it with its informal approach . More than the Complex Analysis that I learnt, and which is peripheral to my main interest, I learnt a lot about Geometric approach to solving many mathematics problems.
Good, insightful expositions of relationship between Geometry and Complex Arithmetic, Mobius Transformations, and Vector Fields.
The mathematics content is at about the level of freshman undergraduate and the book is fairly easy "read". In fact, you don't "read" this book; you work throgh it by drawing pictures after pictures to understand the logic.
This is a good preparation for physics graduate students before first courses in Electrodynamics, Mechanics, and Relativity. In addition, those interested in Geometry, Graphics, Visualization will also appreciate the book.
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23 of 23 people found the following review helpful By Viktor Blasjo on April 8, 2005
Format: Paperback
This is a very exciting introduction to complex analysis. Its most striking feature is the many excellent illustrations; pictures are used to explain things whenever possible. Needham is always eager to explain, and also to show meaning. Thus Möbius transformations are not just charming quirks; instead Needham gives a self-contained introduction to non-Euclidean geometry to show them in action. And when one needs to understand analytic functions as flows, then Needham gives a self-contained introduction to the ideas of vector analysis. Because the book always spills over on other topics like this, I keep my copy within reach at all times, as a treasure mine of beautiful, visual explanations of topics even outside of complex analysis proper. This wide scope works very well most of the time but it should be said that there are probably too many minor side topics than are appropriate in a first textbook. Sometimes Needham seems to include results not because they fit in or add something important, but because he has thought of such a pretty proof. But we quickly forgive him, for the book is so extremely loveable, and it is still by far my first choice as a first textbook of complex analysis.
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