- Paperback: 616 pages
- Publisher: Clarendon Press; Reprint 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: 68 customer reviews
- Amazon Best Sellers Rank: #125,925 in Books (See Top 100 in Books)
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Visual Complex Analysis Reprint Edition
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"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.
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Top customer reviews
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.)
There is a mathematical "poetry" to this book that encourages one to see mathematics as an art. We need more math books like this.
Despite the (deliberate) emphasis on mathematical beauty, the book is quite comprehensive, with almost 600 pages and lots of exercises. It would serve as an introductory textbook for a course in complex variables or as a supplement to other courses.
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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