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Visual Complex Analysis

Tristan Needham

November 1998

ISBN: 9780198534464

616 pages

In Stock

Price: £60.00



This radical approach to complex analysis replaces the standard calculational arguments with new geometric arguments. 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.

About the Author(s)

Tristan Needham, Associate Professor, University of San Francisco, USA


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


"[Needham's] highly praised massive book Visual Complex Analysis may still be resounding in the minds of those who have read it. The original approach and the numerous graphics must have left a lasting impression." - Adhemar Bultheel, Mathematical Association of America Reviews

"... a fascinating and refreshing look at a familiar subject... essential reading for anybody with any interest at all in this absorbing area of mathematics." - Times Higher Education Supplement

"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

"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 tradition by silly games with 2x2 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 2x2 matrices—but his are interesting." - Ian Stewart, New Scientist, 11 October 1997

"... an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas from a geometric point of view. The style is lucid, informal, reader-friendly, and rich with helpful images (e.g. the complex derivative as an "amplitwist"). A truly unusual and notably creative look at a classical subject." - Paul Zorn, American Mathematical Monthly

"I was delighted when I came across [Visual Complex Analysis]. As soon as I thumbed through it, I realized that this was the book I was looking for ten years ago." - Ed Catmull, founder of Pixar