Visual complex analysis - Needham, Tristan (New York : Oxford University Press, 2022)
"This new edition of Visual Complex Analysis applies Newton's geometrical methods from the Principia and his concept of ultimate equality to Complex Analysis. It 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 7 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"--