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Visual Complex Analysis

4.5 out of 5 stars 65 customer reviews
ISBN-13: 978-0198534471
ISBN-10: 0198534477
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Editorial Reviews

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


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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Product Details

  • Hardcover: 616 pages
  • Publisher: Oxford University Press (March 27, 1997)
  • Language: English
  • ISBN-10: 0198534477
  • ISBN-13: 978-0198534471
  • Product Dimensions: 6.1 x 1.5 x 9.1 inches
  • Shipping Weight: 2.2 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (65 customer reviews)
  • Amazon Best Sellers Rank: #1,390,294 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

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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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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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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Format: Paperback
Although mathematical visualization has not been as implicitly forbidden in modern mathematics as claimed by Needham, his work is nonetheless highly innovative even besides his wonderful graphs. The reason is that his prose accompanies very well his extraordinary insight and intuition for the subject. It is purposely not extremely rigorous in order to make the presentation smoother. (This is not so bad as many think. Complex analysis is the target of many excellent books which, fortunately, do not all take the same approach. For more rigor see Ahlfors' "Complex Analysis.")
This book can therefore be an ideal way to get started with complex analysis or even to further one's understanding in the subject. If you are looking for a very affordable predecessor with a similar intuitive style, check Flanigan's "Complex Variables."
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