Visual Complex Analysis / Edition 1

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Overview


This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
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Editorial Reviews

From the Publisher

"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

Mathematical Gazette
I can only describe this book as amazing...it is not an exaggeration to say that there are gems in every section...even familiar facts are frequently explained in refreshingly new ways in this wonderful book....If your budget limits you to buying only one mathematics book in a year then make sure that this is the one that you buy.
Times Higher Education Supplement
Newton would have approved....a fascinating and refreshing look at a familiar subject....It is essential reading for anybody with any interest at all in this absorbing area of mathematics.
Mathematical Reviews
This informal style is excellently judged and works extremely well...Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in some field where complex analysis is used.
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Product Details

  • ISBN-13: 9780198534464
  • Publisher: Oxford University Press
  • Publication date: 2/28/1999
  • Edition description: Reprint
  • Edition number: 1
  • Pages: 616
  • Sales rank: 340,328
  • Product dimensions: 9.00 (w) x 6.10 (h) x 1.30 (d)

Meet 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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Table of Contents

1. Geometry and Complex Arithmetic
2. Complex Functions as Transformations
3. Möbius Transformations and Inversion
4. Differentiation: The Amplitwist Concept
5. Further Geometry of Differentiation
6. Non-Euclidean Geometry*
7. Winding Numbers and Topology
8. Complex Integration: Cauchy's Theorem
9. Cauchy's Formula and Its Applications
10. Vector Fields: Physics and Topology
11. Vector Fields and Complex Integration
12. Flows and Harmonic Functions

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Customer Reviews

Average Rating 4.5
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Sort by: Showing all of 3 Customer Reviews
  • Posted February 15, 2013

    For the Visual Learner

    While my headline might make sense based on the title of this book, this book is amazing at providing lots of detailed images getting at the nuts and bolts of what is going on with the spaces when you preform certain complex operations. I purchased this book to accompany the Complex analysis textbook used in my Graduate School course, which while not a bad book focused very heavily on the analysis and often beautiful visual results where skipped over and ignored completely.

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  • Anonymous

    Posted April 7, 2001

    A wonderful book which explain the inner geometrical reason behind complex analysis

    A superb book which clearly explain the simple but profound geometrical ideas which are at the base of complex analysis.

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  • Anonymous

    Posted April 4, 2010

    No text was provided for this review.

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