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Visual Complex Analysis [Paperback]

Tristan Needham
4.1 out of 5 stars  See all reviews (19 customer reviews)
List Price: CDN$ 88.50
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Book Description

Jan. 1 1999 0198534469 978-0198534464 Reprint
Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

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Product Description


`...one very fine recent example of mathematical graphics at a high level is Needham's Visual Complex Analysis.' Notices of the AMS

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numerous line drawings

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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

Most helpful customer reviews
2 of 2 people found the following review helpful
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
4.0 out of 5 stars Lots of material, great pictures but too chatty March 2 2004
By A Customer
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
4.0 out of 5 stars amazing visual representations Oct. 8 2001
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
3.0 out of 5 stars Overly geometric May 9 2001
By A Customer
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
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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Most recent customer reviews
5.0 out of 5 stars A marvel, eye-popping, fun. More than five stars!
What a great book this is!
This is a book that any math afficionado must have, and will undoubtedly savor. Read more
Published on Jan. 9 2004 by Paul J. Papanek
5.0 out of 5 stars Where do I send the 50-cent soda for the book?!
This book does an exceptional job of giving a hands-on person an opportunity to "see" what is happening in complex analysis. Read more
Published on Aug. 21 2003 by Chip Smith
5.0 out of 5 stars excellent book on this subject
i am not a philisopher like some reviewers here...this book is really wonderful and even better.
the subject is very clearly explained in a very educational manner. Read more
Published on Aug. 8 2003 by Ahmed Morsi
1.0 out of 5 stars A barely tolerable door stop
I bought this book in conjuction with a class on complex mathematics I took at a university. Within two classes I had abandoned all hope of actually learning something and by... Read more
Published on Aug. 6 2003
5.0 out of 5 stars A great marvel
This is a marvelous presentation of the subject. After looking at many analysis books which require a great deal of coffee to accompany them, I was surprised to find a book that... Read more
Published on June 26 2003 by Dima
3.0 out of 5 stars Hm.......
Th merits of this book has been well talked by others, I have few to add to. My question is, in order to distinguish the text, does the author distort the history of the subject? Read more
Published on June 8 2003
5.0 out of 5 stars Gee, a math book that really teaches, how unusual
I tried to learn complex analysis from Ahlfors, I wouldn't recommend you try it although it is a good book. Read more
Published on April 22 2003 by Carl F. Mclaren Jr.
5.0 out of 5 stars What a beauty!
This is one hell of a book. Needham explains the geometrical concept of complex numbers and functions in a highly visual way. Read more
Published on Nov. 26 2002 by "jayjina"
5.0 out of 5 stars One book to read...
If somebody ask you to choose one book, because you are going to live the rest of your live in Mars, choose this one.
Published on Oct. 16 2002 by Juan Gustavo Sanchez
5.0 out of 5 stars Best math book I've read in years!
I have recently finished reading this book cover-to-cover and, in spite of having worked
in mathematical physics for 40 years, feel compelled to gush like a teenager. Read more
Published on Sept. 29 2002 by Gerald Kaiser
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