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Zusatztext "McGehee discusses the basics of complex variables and a few applications to physics in a rigorous and understandable manner." (Choice Vol. 38! No. 8! April 2001)A versatile textbook offering all the material...for a first course...in complex analysis but also containing some more avanced material in the final chapter. (Aslib Book Guide! May 2001! Vol 66! No 5)"...sophisticated approach that stresses the geometry of complex mappings." (Journal of Natural Products American Mathematical Monthly! November 2001) Informationen zum Autor O. Carruth McGehee is the author of An Introduction to Complex Analysis, published by Wiley. Klappentext Recent decades have seen profound changes in the way we understand complex analysis. This new work presents a much-needed modern treatment of the subject, incorporating the latest developments and providing a rigorous yet accessible introduction to the concepts and proofs of this fundamental branch of mathematics. With its thorough review of the prerequisites and well-balanced mix of theory and practice, this book will appeal both to readers interested in pursuing advanced topics as well as those wishing to explore the many applications of complex analysis to engineering and the physical sciences.* Reviews the necessary calculus, bringing readers quickly up to speed on the material* Illustrates the theory, techniques, and reasoning through the use of short proofs and many examples* Demystifies complex versus real differentiability for functions from the plane to the plane* Develops Cauchy's Theorem, presenting the powerful and easy-to-use winding-number version* Contains over 100 sophisticated graphics to provide helpful examples and reinforce important concepts Zusammenfassung Die komplexe Analysis wird in vielen Bereichen der Physik und Technik angewendet. Eine effiziente, straffe, mathematisch exakte und trotzdem gut verständliche Einführung in dieses Gebiet erhalten Sie mit diesem Band. Studenten mit mageren Vorkenntnissen finden durch ein einleitendes Kapitel schnell den Anschluß. Alle Konzepte werden durch hervorragende Illustrationen veranschaulicht. (11/00) Inhaltsverzeichnis Preliminaries. Basic Tools. The Cauchy Theory. The Residue Calculus. Boundary Value Problems. Lagniappe. References. Index....
