Название: Visual Complex Analysis: 25th Anniversary Edition
Автор: Tristan Needham
Издательство: Oxford University Press
Год: 2023
Страниц: 720
Язык: английский
Формат: pdf
Размер: 14.4 MB

The 25th Anniversary Edition features a new Foreword by Sir Roger Penrose, as well as a new Preface by the author.

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!

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.

"The new ideas and exercises bring together a body of information potentially invaluable to researchers in fields from topology to number theory... this is only the beginning of a long list of famous facts for which Needham offers attractive visual proofs: Cauchy's theorem is a satisfying example: you can see the contribution to the integral from each infinitesimal square vanish before your eyes." -- Frank Farris, American Mathematical Monthly

"This informal style is excellently judged and works extremely well. Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in any field where complex analysis is used." -- David Armitage, Mathematical Reviews

"The arguments constructed are highly innovative; even veterans of the field will find new ideas here. This is a special book. Tristan Needham has not only completely rethought a classical field of mathematics, but has presented it in a clear and compelling way. Visual Complex Analysis is worthy of the accolades it has received" -- MAA Reviews