Complex Analysis (The Hitch Hiker's Guide to the Plane

• Main Authors: Stewart, Ian 1945- (Author), Tall, David Orme (Author)
• Format: Book
• Language: English
• Published: New York, NY Cambridge University Press 2018; ©1983; ©2018
• Edition: Second edition
• Subjects: Functions of complex variables; Numbers, Complex; Geometry, Analytic |x Plane
• Online Access: Click Here to View Status and Holdings.
• Physical Description: xiii, 389 pages illustrations 25 cm
• Bibliography: Includes bibliographical references (page 382) and index
• ISBN: 9781108436793

This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise as a result of the richer geometry of the complex plane. Key features of the authors' approach are to use simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, to address the conceptual conflicts between pure and applied approaches head-on. Beyond the material of the clarified and corrected original edition, there are three new chapters: Chapter 15, on infinitesimals in real and complex analysis; Chapter 16, on homology versions of Cauchy's theorem and Cauchy's residue theorem, linking back to geometric intuition; and Chapter 17, outlines some more advanced directions in which complex analysis has developed, and continues to evolve into the future. With numerous worked examples and exercises, clear and direct proofs, and a view to the future of the subject, this is an invaluable companion for any modern complex analysis course.