Coloring Book Of Complex Function Representations

Author : Julie Barnes
Publisher : MAA Press
ISBN 13 : 9780883855911
Total Pages : 40 pages
Book Rating : 4.17/5 ( download)

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Download or read book Coloring Book of Complex Function Representations written by Julie Barnes and published by MAA Press. This book was released on 2017-12-31 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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!

Author : Diana Davis
Publisher : American Mathematical Soc.
ISBN 13 : 1470461226
Total Pages : 171 pages
Book Rating : 4.25/5 ( download)

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Download or read book Illustrating Mathematics written by Diana Davis and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Elias Wegert
Publisher : Springer Science & Business Media
ISBN 13 : 3034801807
Total Pages : 374 pages
Book Rating : 4.05/5 ( download)

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Download or read book Visual Complex Functions written by Elias Wegert and published by Springer Science & Business Media. This book was released on 2012-08-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Bernd Thaller
Publisher : Springer Science & Business Media
ISBN 13 : 0387227709
Total Pages : 283 pages
Book Rating : 4.02/5 ( download)

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Download or read book Visual Quantum Mechanics written by Bernd Thaller and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : William Johnston
Publisher : American Mathematical Society
ISBN 13 : 1470465655
Total Pages : 456 pages
Book Rating : 4.50/5 ( download)

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Download or read book The Calculus of Complex Functions written by William Johnston and published by American Mathematical Society. This book was released on 2022-04-01 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Sam Damron
Publisher :
ISBN 13 : 9781980985822
Total Pages : 48 pages
Book Rating : 4.20/5 ( download)

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Download or read book Trig Function Coloring Book written by Sam Damron and published by . This book was released on 2018-05-10 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Far from the boring sine and cosine functions you learned in high school, this book presents the swirling beauty of trigonometric functions for your coloring enjoyment. Sine, cosine, and tangent romp through this book, along with their playful counterparts cosecant, secant, and cotangent. Other fabulous functions also make a guest appearance! Hours of coloring entertainment, perfect for both math and art lovers!

Author : Richard Beals
Publisher : Springer Nature
ISBN 13 : 3030545334
Total Pages : 353 pages
Book Rating : 4.38/5 ( download)

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Download or read book Explorations in Complex Functions written by Richard Beals and published by Springer Nature. This book was released on 2020-10-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.

Author : B. D. Wilkins
Publisher : WIT Press
ISBN 13 : 1784664510
Total Pages : 290 pages
Book Rating : 4.10/5 ( download)

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Download or read book Excel in Complex Variables with the Complex Variable Boundary Element Method written by B. D. Wilkins and published by WIT Press. This book was released on 2021-09-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hans Colonius
Publisher : Psychology Press
ISBN 13 : 1136871780
Total Pages : 259 pages
Book Rating : 4.88/5 ( download)

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Download or read book Measurement and Representation of Sensations written by Hans Colonius and published by Psychology Press. This book was released on 2013-05-13 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Roger Penrose
Publisher : Vintage
ISBN 13 : 0593315308
Total Pages : 1136 pages
Book Rating : 4.09/5 ( download)

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Download or read book The Road to Reality written by Roger Penrose and published by Vintage. This book was released on 2021-06-09 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: **WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin