Visual Complex Analysis : 25th Anniversary Edition

Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new way^DDLas a highbrow comic book! Copyright Foreword Preface to the 25th Anniversary Edition Preface Acknowledgements Contents Chapter 1 Geometry and Complex Arithmetic Chapter 2 Complex Functions as Transformations Chapter 3 Mobius Transformations and Inversion Chapter 4 Differentiation: The Amplitwist Concept Chapter 5 Further Geometry of Differentiation Chapter 6 Non-Euclidean Geometry Chapter 7 Winding Numbers and Topology Chapter 8 Complex Integration: Cauchy's Theorem Chapter 9 Cauchy's Formula and Its Applications Chapter 10 Vector Fields: Physics and Topology Chapter 11 Vector Fields and Complex Integration Chapter 12 Flows and Harmonic Functions Bibliography Index This new 25th anniversary edition of Visual Complex Analysis introduces this powerful method combining complex numbers with ordinary calculus, and includes new introductory content and brand-new captions that fully explain the geometrical reasoning.