Complex Analysis

Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick and a Fellow of the Royal Society. He has five honorary doctorates and is an honorary wizard of Unseen University. His more than 130 books include Professor Stewart's Cabinet of Mathematical Curiosities and the four-volume series The Science of Discworld with Terry Pratchett and Jack Cohen. His SF novels include the trilogy Wheelers, Heaven, and Oracle (with Jack Cohen), The Living Labyrinth and Rock Star (with Tim Poston), and Jack of All Trades. Short story collections are Message from Earth and Pasts, Presents, Futures. His Flatland sequel Flatterland has extensive fantasy elements. He has published 33 short stories in Analog, Omni, Interzone, and Nature, with 10 stories in Nature's 'Futures' series. He was Guest of Honour at Novacon 29 in 1999 and Science Guest of Honour and Hugo Award Presenter at Worldcon 75 in Helsinki in 2017. He delivered the 1997 Christmas Lectures for BBC television. His awards include the Royal Society's Faraday Medal, the Gold Medal of the IMA, the Zeeman Medal, the Lewis Thomas Prize, the Euler Book Prize, the Premio Internazionale Cosmos, the Chancellor's Medal of the University of Warwick, and the Bloody Stupid Johnson Award for Innovative Uses of Mathematics.

Preface to the first edition; Preface to the second edition; The origins of complex analysis, and its challenge to intuition; 1. Algebra of the complex plane; 2. Topology of the complex plane; 3. Power series; 4. Differentiation; 5. The exponential function; 6. Integration; 7. Angles, logarithms, and the winding number; 8. Cauchy's theorem; 9. Homotopy versions of Cauchy's theorem; 10. Taylor series; 11. Laurent series; 12. Residues; 13. Conformal transformations; 14. Analytic continuation; 15. Infinitesimals in real and complex analysis; 16. Homology version of Cauchy's theorem; 17. The road goes ever on; References; Index.