Coloring Book Of Complex Function Representations
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Coloring Book Of Complex Function Representations
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Author : Julie Barnes
language : en
Publisher: MAA Press
Release Date : 2017-12-31
Coloring Book Of Complex Function Representations written by Julie Barnes and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-31 with categories.
Have you ever seen a mathematical object that was so intriguing that anyone, regardless of mathematical background, could appreciate its aesthetic beauty? If so, did you stop to color it? Now is your chance. Explore the beauty of mathematics in this collection if intricate pictures related to complex-valued functions. Any of these images could pass for designs found in some of the many coloring books for adults seen in stores today and are displayed here for you to color. While looking at the coloring pages, you can read about the author's quest to find interesting images. Their tale includes expeditions on the complex plane, work with families of complex functions, visits to Julia sets, unexpected results from a typo, random explorations, and a final send-off from a well-known cartoon character. Grab your colored pencils and enjoy coloring these functions. There are no incorrect ways to color, and consequently, there are no answers in the back of the book!
Visual Complex Functions
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Author : Elias Wegert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-30
Visual Complex Functions written by Elias Wegert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-30 with Mathematics categories.
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.
Illustrating Mathematics
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Author : Diana Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-16
Illustrating Mathematics written by Diana Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Education categories.
This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
Visual Complex Functions
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Author : Elias Wegert
language : en
Publisher: Birkhäuser
Release Date : 2012-08-29
Visual Complex Functions written by Elias Wegert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.
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.
The Calculus Of Complex Functions
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Author : William Johnston
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-01
The Calculus Of Complex Functions written by William Johnston and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Methods Of The Theory Of Functions Of Many Complex Variables
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Author : Vasiliy Sergeyevich Vladimirov
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Methods Of The Theory Of Functions Of Many Complex Variables written by Vasiliy Sergeyevich Vladimirov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Visual Quantum Mechanics
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Author : Bernd Thaller
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Visual Quantum Mechanics written by Bernd Thaller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Science categories.
"Visual Quantum Mechanics" uses the computer-generated animations found on the accompanying material on Springer Extras to introduce, motivate, and illustrate the concepts explained in the book. While there are other books on the market that use Mathematica or Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner. There is no special emphasis on computational physics or requirement that the reader know a symbolic computation package. Despite the presentation of rather advanced topics, the book requires only calculus, making complicated results more comprehensible via visualization. The material on Springer Extras provides easy access to more than 300 digital movies, animated illustrations, and interactive pictures. This book along with its extra online materials forms a complete introductory course on spinless particles in one and two dimensions.
The Processing Of Relationally Complex Representations
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Author : James Kenneth Kroger
language : en
Publisher:
Release Date : 1998
The Processing Of Relationally Complex Representations written by James Kenneth Kroger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Excel In Complex Variables With The Complex Variable Boundary Element Method
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Author : B. D. Wilkins
language : en
Publisher: WIT Press
Release Date : 2021-09-22
Excel In Complex Variables With The Complex Variable Boundary Element Method written by B. D. Wilkins and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-22 with Mathematics categories.
Using the familiar software Microsoft ® Excel, this book examines the applications of complex variables. Implementation of the included problems in Excel eliminates the “black box” nature of more advanced computer software and programming languages and therefore the reader has the chance to become more familiar with the underlying mathematics of the complex variable problems. This book consists of two parts. In Part I, several topics are covered that one would expect to find in an introductory text on complex variables. These topics include an overview of complex numbers, functions of a complex variable, and the Cauchy integral formula. In particular, attention is given to the study of analytic complex variable functions. This attention is warranted because of the property that the real and imaginary parts of an analytic complex variable function can be used to solve the Laplace partial differential equation (PDE). Laplace's equation is ubiquitous throughout science and engineering as it can be used to model the steady-state conditions of several important transport processes including heat transfer, soil-water flow, electrostatics, and ideal fluid flow, among others. In Part II, a specialty application of complex variables known as the Complex Variable Boundary Element Method (CVBEM) is examined. CVBEM is a numerical method used for solving boundary value problems governed by Laplace's equation. This part contains a detailed description of the CVBEM and a guide through each step of constructing two CVBEM programs in Excel. The writing of these programs is the culminating event of the book. Students of complex variables and anyone with an interest in a novel method for approximating potential functions using the principles of complex variables are the intended audience for this book. The Microsoft Excel applications (including simple programs as well as the CVBEM program) covered will also be of interest in the industry, as these programs are accessible to anybody with Microsoft Office.
Measurement And Representation Of Sensations
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Author : Hans Colonius
language : en
Publisher: Psychology Press
Release Date : 2013-05-13
Measurement And Representation Of Sensations written by Hans Colonius and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Psychology categories.
Measurement and Representation of Sensations offers a glimpse into the most sophisticated current mathematical approaches to psychophysical problems. In this book, editors Hans Colonius and Ehtibar N. Dzhafarov, top scholars in the field, present a broad spectrum of innovative approaches and techniques to classical problems in psychophysics at different levels of stimulus complexity. The chapters emphasize rigorous mathematical constructions to define psychophysical concepts and relate them to observable phenomena. The techniques presented, both deterministic and probabilistic, are all original and recent. Subjects addressed throughout the six chapters of this volume include: *computing subjective distances from discriminability; *a new psychophysical theory of intensity judgments; *computing subjective distances from two discriminability functions; *an alternative to the model-building approach based on observable probabilities; and *possible forms of perceptual separability developed within a generalization of General Recognition Theory. Measurement and Representation of Sensations is a valuable text for both behavioral scientists and applied mathematicians.