Complex Integration And Cauchy's Theorem (1914)

Complex Integration And Cauchy�������s Theorem is a book written by G. N. Watson and first published in 1914. It is a comprehensive and detailed treatment of the theory of complex integration and Cauchy's theorem, which are important topics in complex analysis. The book is divided into three parts, each of which covers a different aspect of the theory. The first part of the book deals with the basic concepts of complex analysis, including the definition of complex numbers, the Cauchy-Riemann equations, and the properties of analytic functions. The second part of the book focuses on the theory of complex integration, including contour integration, Cauchy's theorem, and the Cauchy integral formula. The third and final part of the book covers advanced topics in complex analysis, including the theory of entire functions, the Riemann mapping theorem, and the theory of conformal mapping.Throughout the book, Watson provides clear and concise explanations of the theory, along with numerous examples and exercises to help readers understand and apply the concepts. The book is written for advanced undergraduate and graduate students in mathematics, as well as researchers and professionals in the field of complex analysis. Despite being over a century old, Complex Integration And Cauchy�������s Theorem remains a valuable resource for anyone interested in the theory of complex analysis.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Originally published in 1914 as number fifteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise proof of Cauchy's Theorem, along with some applications of the theorem to the evaluation of definite integrals.