Visual Complex Functions

An Introduction with Phase Portraits

Elias Wegert

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English

Springer Basel
28 August 2012

Mathematics & Sciences; Complex analysis, complex variables; Functional analysis & transforms

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.

By: Elias Wegert
Imprint: Springer Basel
Country of Publication: Switzerland
Edition: 2012
Dimensions: Height: 240mm, Width: 168mm, Spine: 18mm
Weight: 780g
ISBN: 9783034801799
ISBN 10: 3034801793
Pages: 374
Publication Date: 28 August 2012
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Elias Wegert is a Professor of Mathematics at the Technische Universitat 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.

Reviews for Visual Complex Functions: An Introduction with Phase Portraits

From the reviews: This textbook is an introduction to the classical theory of functions of one complex variable. Its distinctive feature are the graphical representations of functions, being the most useful tool in teaching and generally in mathematics. ... The self-sufficiency of the textbook and the broad range of graphical examples makes the book useful for students as well as teachers of mathematics. ... the book can be warmly recommended both to experts and to a new generation of mathematicians. (Stanislawa Kanas, Zentralblatt MATH, Vol. 1264, 2013)