Visual Complex Analysis - Tristan Needham

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Résumé :
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-as a highbrow comic book!...

Biographie:
Tristan Needham (son of the distinguished social anthropologist Rodney Needham) grew up in Oxford, England. He studied physics at Merton College, Oxford, before moving to the Mathematical Institute, where he enjoyed the great privilege of studying black holes under the supervision of Sir Roger Penrose. Tristan received his DPhil in 1987 and joined the faculty of the University of San Francisco in 1989. His continuing mission is to seek out new intuitive forms of understanding, and new visualizations....

Sommaire:

• 1: Geometry and Complex Arithmetic
• 2: Complex Functions as Transformations
• 3: M?bius 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