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Visual Complex Functions: An Introduction With Phase Portraits (Anglais) Broché – 29 août 2012


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Description du produit

Revue de presse

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)

Anyone who works with complex variables should read this book. ... Visual Complex Functions is a beautiful and careful presentation of an entire advanced introduction to complex analysis based on phase portraits and, where appropriate, other kinds of computer-generated pictures. ... My understanding of many ideas and phenomena deepened through reading this book. --(Lloyd N. Trefethen, SIAM Review, Vol. 55 (4), 2013)

Présentation de l'éditeur

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.

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Commentaires client les plus utiles sur Amazon.com

Amazon.com: 5,0 sur 5 étoiles 3 commentaires
10 personnes ont trouvé cela utile.
5,0 sur 5 étoilesUseful supplement for your complex analysis class
le 17 novembre 2014 - Publié sur Amazon.com
25 personnes ont trouvé cela utile.
5,0 sur 5 étoilesmust-read for anyone working with complex functions
le 16 mars 2013 - Publié sur Amazon.com
2 personnes ont trouvé cela utile.
5,0 sur 5 étoilesAn excellent complementary to traditional complex analysis text
le 15 décembre 2016 - Publié sur Amazon.com
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