Visual Complex Analysis
Tristan Needham, Roger Penrose
Abstract
Abstract The fundamental advance in the new 25th Anniversary Edition is that the original 501 diagrams now include 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! The new edition openly challenges the current dominance of purely symbolic logical reasoning by using new, visually accessible arguments to explain the truths of elementary complex analysis. The first seven chapters discuss geometry and complex arithmetic; complex functions as transformations; Möbius transformations and inversion; differentiation and the amplitwist concept; non-Euclidean geometry; and winding numbers and topology. The book then turns to an examination of complex integration and Cauchy’s Theorem; Cauchy’s Formula and its applications; vector fields; and flows and harmonic functions. To provoke curiosity, exercises can be found at the end of each chapter, allowing readers to develop considerable computational skills. These exercises also illustrate how geometric thinking can often replace lengthy calculation.