Visual Complex Analysis

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.

1. Geometry and Complex Arithmetic; 2. Complex functions as Transformations; 3. Mobius 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: Cuachy'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

... 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

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