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Visual Complex Analysis

PDF Download Visual Complex Analysis

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Review

"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

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About the Author

Tristan Needham is Associate Professor of Mathematics at the University of San Francisco. For part of the work in this book, he was presented with the Carl B. Allendoerfer Award by the Mathematical Association of America.

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Product details

Paperback: 616 pages

Publisher: Clarendon Press; New Ed 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: 3.5 pounds (View shipping rates and policies)

Average Customer Review:

4.1 out of 5 stars

74 customer reviews

Amazon Best Sellers Rank:

#53,793 in Books (See Top 100 in Books)

The two stars are not for the book, which is a masterpiece of exposition. It's a brilliant introduction to this topic, creating an intuitive feel for its methods and ideas through provocative geometric arguments. My low rating is for the kindle version: those wonderful geometric arguments are made more wonderful by helpful and ingenious diagrams, many of which don't get reproduced in the digital version. Without the figures to guide a reader, the exposition is compromised: when he refers to diagram X and you can't see diagram X, what follows is hard to read. Save the money and buy the print version. And then get ready for Needham to blow your mind! You'll never see Calculus/Analysis the same way again.

I LOVE the printed, paper copy, it is absolutely among the best math book I've ever studied. Been waiting for a Kindle version for a long time. But the electronic version is of a low quality, it can not display pages properly, feels like a xeroxed copy of the original book!!!

I have held off on writing a review on this book for some time now. After having read it completely, and, more importantly, having worked with complex variables extensively, I am finally ready to deliver a verdict on it.I applaud the author's effort to visually describe the complex plane: in particularly complex multiplication and integration. He also goes into great detail on Mobius transformations and other geometric concepts. However, I think that he missed the opportunity to describe complex differentials completely. While he speaks of analytic functions being "everywhere aplitwist," he doesn't describe the nature of differentials at analytic points: namely, the differential remains the same, regardless of which path we take from the point. This much more clearly explains the rigidity of analytic functions (along with theorems like FTC, maximum modulus, etc. which follow directly from this rigidity).I believe that he forsakes his own thesis in describing the argument principle in generic topological arguments. These arguments are far more involved than they need to be.More than anything, I dislike how he uses results that haven't been proved. It is quite annoying to use Cauchy's Theorem throughout the book, not proving it till very late.All that said, this is an overall great book that will get you thinking about the concepts. His writing style is very skillful, and, obviously, he provides a lot of figures to help get his point across. It is definitely worth adding to your library, but I think that you will need at least one other text to completely grasp the subject. (I personally recommend Gamelin's book.)

I first read this book in 2001. I have now re-read it and I hope to re-read it many more times. This is an exceptional book and I am dumbfounded by how illuminating it has been with a second read 11 years later. The author makes a distinct effort to provide deep (principally geometric) insights into complex analysis as well as connections between complex analysis and non-Euclidean geometry as well as physics. The power of visualization and the amplitwist concept is clear. I still need to re-read this book to get the most out of it but the explorations of conformal mappings/analyticity/harmonic functions from the multiple viewpoints was a unique and deeply rewarding experience.See the website: [...]

Complex analysis can challenge the intuition of the new student. This text is unique, among high quality textbooks, in giving a careful and thorough exploration of the geometric meaning underlying the usual algebra and calculus of complex numbers. The Cauchy-Riemann equations define what is meant by a holomorphic function. Restricting to these particularly pleasant and useful functions, the formalism of calculus looks very much like ordinary calculus. Too many students muddle through complex analysis with the notion that it looks like calculus, except some extra nice functions also hold. Such students commonly become competent, but they seldom actually get good at complex analysis. In particular, for many engineers, complex calculus remains an unpalatable mystery, even though they know how to do the calculations. That is the difficulty, and Needham corrects the whole of the difficulty perfectly.Ahlfors is a great classical text. Conway (two volumes) is thorough, clear, and modern. Carrier, Krook, and Pearson is especially concise and well oriented to the practical calculations of engineering and applied science. Berenstein/Gay is very modern and oriented to a very high quality undergraduate or beginning graduate who intends to continue in (very) pure mathematics. All these and more (e.g. Saff) are at least very good or perhaps excellent texts. Because there is a body of problems that beginners are expected to be able to work (mathematics is also a culture---there are expectations), it is probably necessary to pick one of these texts and to use Needham's book as one of two texts for an excellent course. I know of no other book that gives the great intuitive and geometric understanding of complex analysis that Needham gives. I would, under no circumstances, teach any beginning course in complex analysis at any school anywhere at any time for any reason without using Needham as one of the texts. If I were feeling particularly self-satisfied, I might possibly use it as the only text. I myself seldom feel so confident. Perhaps you do. This text is used frequently at M.I.T. and at Oxford. That seems to me a great recommendation. The book is very well and clearly written. The prose flows. It is a great joy to read.

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