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Visual Complex Analysis Paperback – Jan 1 1999


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Product Details

  • Paperback: 616 pages
  • Publisher: Clarendon Press; Reprint edition (Jan. 1 1999)
  • Language: English
  • ISBN-10: 0198534469
  • ISBN-13: 978-0198534464
  • Product Dimensions: 3.1 x 15 x 22.5 cm
  • Shipping Weight: 862 g
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Bestsellers Rank: #209,276 in Books (See Top 100 in Books)
  • See Complete Table of Contents


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First Sentence
Four and a half centuries have elapsed since complex numbers were first discovered. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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2 of 2 people found the following review helpful By Christopher G. Moore on Oct. 2 2003
Format: Paperback
I used this book in an introductory Complex Variables course in a top 20 ranked US college. I enjoyed the authors clear explaination of material and clearly british sense of humor. Unfortunately I felt it lacked a great deal of rigor. Proofs were often either just sketched or pictorally shown. I understand that it was the author's objective to give a purely goemetric approach, but I felt that more detail was needed. When I needed to use ideas such as residue classes and other important complex variable conecepts in later math courses, my background was weak.
I agree that the book does have merits. It takes the field of complex variables and looks at it in another way. I do feel though, that a more traditional book would be better to first secure undersatanding of the material. If a student were to continue to graduate work or want to learn more about complex variables, this would be a good supplement. I do not feel though, that this book is a good main, first text.
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1 of 1 people found the following review helpful By A Customer on March 2 2004
Format: Hardcover
I purchased this book as a reference and because of it's coverage on Mobius Transformations, which is great! My qualms are with the other parts of the book, however. I'll reach for this book or Churchill and Brown when I'm dealing with complex numbers. Browns is much more direct and to the point. There are times that I'll have to flip through several pages jsut to get to the point. Needham often includes a history of the topic and several applications before getting to the mathematics of it. I like reading about applications at the end of the chapters and histories as footnotes (or both in a completely seperate part of the book, i.e. the appendix). If you buy this book, you'll get a lot of great mathematics and wonderful visualizations, but expect a lot of reading that may not be immidiately necessary to your studies.
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1 of 1 people found the following review helpful By UNPINGCO on Oct. 8 2001
Format: Paperback
This text provides sometimes amazing visual representations of concepts in complex analysis that I have never seen anywhere else. For example, I have never seen a complex contour integral interpreted geometrically. Also, the text presents many very important conformal maps. Having said that, however, I would not recommend this as a first book in complex analysis. A better first book along these same visual lines, but with more rigor is Flanigan's "Complex Analysis". On the other hand, if you already have a more traditional grounding in complex analysis and want to motivate many of the results geometrically, then this book is uniquely suited for that. This book provides useful "explanations" and not rigorous proofs.
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1 of 1 people found the following review helpful By A Customer on May 9 2001
Format: Paperback
I have enjoyed working through this book. As others have pointed out, it's a nice geometric introduction to complex analysis. I do, however, have a couple gripes. One major and one very minor.
First, Needham seems to strive for a kind of geometric "purity". He tries to give the impression that geometric arguments are more valid than standard logic or algebra. While some might feel this is a needed correction to alleged anti-geometric trends in math, Needham's correction can, at times, be an overreaction.
The result is that the book is excellent in those areas that are well-suited to a geometric approach (e.g. Mobius transformations and hyperbolic geometry), but fails in areas for which algebraic approaches are simpler and easier to understand. Parts of the chapters on differentiation are unnecessarily cumbersome. (While the "amplitwist" thing --- a geometric version of complex-differentiation-as-local-multiplication --- is neat, it's a little overdone, and ends up making differentiation sound more mysterious than it is.)
Insisting on "pure" geometric arguments is a nice exercise. But when it obscures the subject and makes it more difficult to follow, one begins to see why math has moved away from that kind of reasoning over the past several hundred years. By the time I finished Needham's book, my appreciation for non-geometric mathematics had increased quite a bit.
In any case, I think students could learn well from certain chapters of this book (the more geometric ones), but should definitely be steered away from others (differentiation and integration). This would make a great supplementary text but not a good main text.
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1 of 1 people found the following review helpful By Shankar N. Swamy on Aug. 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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