Visual Complex Functions. An Introduction with Phase Portraits

Wegert, Elias:

ISBN 10: 3034801793 / ISBN 13: 9783034801799

Published by Basel, Birkhäuser, 2012

About this Item

Formateinband: Paperback / kartonierte Ausgabe XIV, 360 S. (24 cm) 1st Edition; Sehr guter Zustand. Sprache: Englisch Gewicht in Gramm: 950 [Stichwörter: Complex functions, Analytic functions, Complex calculus, Construction principles, Conformal mappings, Riemann surfaces]. Seller Inventory # 74024

Bibliographic Details

Title: Visual Complex Functions. An Introduction ...

Publisher: Basel, Birkhäuser

Publication Date: 2012

Binding: Soft cover

Condition: Sehr gut

Edition: 1st Edition

About this title

Synopsis:

This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains.

Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes.

In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions.

Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

About the Author:

Elias Wegert is a Professor of Mathematics at the Technische Universität Bergakademie Freiberg. His main research interests are in Complex and Nonlinear Analysis; he is the author of a book on nonlinear Riemann-Hilbert problems and their applications. Wegert has experience in mathematical teaching at different levels for about 30 years. He is also committed to mathematical competitions for high school students.