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Explorations In Complex Functions
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Book Synopsis More Explorations in Complex Functions by : Richard Beals
Download or read book More Explorations in Complex Functions written by Richard Beals and published by Springer Nature. This book was released on 2023-07-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year’s course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange’s theorem, respectively. Chapters 5—7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10–14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann—Hilbert problem and integral equations, and Darboux’s method for computing asymptotics.
Book Synopsis Explorations in Complex Functions by : Richard Beals
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.
Book Synopsis Geometric Function Theory by : Steven G. Krantz
Download or read book Geometric Function Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2007-09-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations
Book Synopsis Explorations in Complex Analysis by : Michael A. Brilleslyper
Download or read book Explorations in Complex Analysis written by Michael A. Brilleslyper and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
Book Synopsis Geometric Function Theory by : Steven G. Krantz
Download or read book Geometric Function Theory written by Steven G. Krantz and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Visual Complex Functions by : Elias Wegert
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 360 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.
Book Synopsis Explorations In Numerical Analysis: Python Edition by : James V Lambers
Download or read book Explorations In Numerical Analysis: Python Edition written by James V Lambers and published by World Scientific. This book was released on 2021-01-14 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Book Synopsis Language is a complex adaptive system: Explorations and evidence by : Kristine Lund
Download or read book Language is a complex adaptive system: Explorations and evidence written by Kristine Lund and published by Language Science Press. This book was released on 2022-10-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ASLAN labex - Advanced studies on language complexity - brings together a unique set of expertise and varied points of view on language. In this volume, we employ three main sections showcasing diverse empirical work to illustrate how language within human interaction is a complex and adaptive system. The first section – epistemological views on complexity – pleads for epistemological plurality, an end to dichotomies, and proposes different ways to connect and translate between frameworks. The second section – complexity, pragmatics and discourse – focuses on discourse practices at different levels of description. Other semiotic systems, in addition to language are mobilized, but also interlocutors’ perception, memory and understanding of culture. The third section – complexity, interaction, and multimodality – employs different disciplinary frameworks to weave between micro, meso, and macro levels of analyses. Our specific contributions include adding elements to and extending the field of application of the models proposed by others through new examples of emergence, interplay of heterogeneous elements, intrinsic diversity, feedback, novelty, self-organization, adaptation, multi-dimensionality, indeterminism, and collective control with distributed emergence. Finally, we argue for a change in vantage point regarding the search for linguistic universals.
Book Synopsis Introduction to the Theory of Complex Functions by : Jian-Ke Lu
Download or read book Introduction to the Theory of Complex Functions written by Jian-Ke Lu and published by World Scientific. This book was released on 2002 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. For instance, the multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where poles of analytic functions considered may occur on the boundary of a region ? which is very useful in applications but not seen in textbooks written in English.
Book Synopsis Current Topics in Pure and Computational Complex Analysis by : Santosh Joshi
Download or read book Current Topics in Pure and Computational Complex Analysis written by Santosh Joshi and published by Springer. This book was released on 2014-12-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains 13 articles, some of which are survey articles and others research papers. Written by eminent mathematicians, these articles were presented at the International Workshop on Complex Analysis and Its Applications held at Walchand College of Engineering, Sangli. All the contributing authors are actively engaged in research fields related to the topic of the book. The workshop offered a comprehensive exposition of the recent developments in geometric functions theory, planar harmonic mappings, entire and meromorphic functions and their applications, both theoretical and computational. The recent developments in complex analysis and its applications play a crucial role in research in many disciplines.
Book Synopsis Explorations in Complex and Riemannian Geometry by : John Bland
Download or read book Explorations in Complex and Riemannian Geometry written by John Bland and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Book Synopsis The Calculus of Complex Functions by : William Johnston
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.
Book Synopsis Computational Explorations in Cognitive Neuroscience by : Randall C. O'Reilly
Download or read book Computational Explorations in Cognitive Neuroscience written by Randall C. O'Reilly and published by MIT Press. This book was released on 2000-08-28 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text, based on a course taught by Randall O'Reilly and Yuko Munakata over the past several years, provides an in-depth introduction to the main ideas in the computational cognitive neuroscience. The goal of computational cognitive neuroscience is to understand how the brain embodies the mind by using biologically based computational models comprising networks of neuronlike units. This text, based on a course taught by Randall O'Reilly and Yuko Munakata over the past several years, provides an in-depth introduction to the main ideas in the field. The neural units in the simulations use equations based directly on the ion channels that govern the behavior of real neurons, and the neural networks incorporate anatomical and physiological properties of the neocortex. Thus the text provides the student with knowledge of the basic biology of the brain as well as the computational skills needed to simulate large-scale cognitive phenomena. The text consists of two parts. The first part covers basic neural computation mechanisms: individual neurons, neural networks, and learning mechanisms. The second part covers large-scale brain area organization and cognitive phenomena: perception and attention, memory, language, and higher-level cognition. The second part is relatively self-contained and can be used separately for mechanistically oriented cognitive neuroscience courses. Integrated throughout the text are more than forty different simulation models, many of them full-scale research-grade models, with friendly interfaces and accompanying exercises. The simulation software (PDP++, available for all major platforms) and simulations can be downloaded free of charge from the Web. Exercise solutions are available, and the text includes full information on the software.
Book Synopsis Harmonic and Complex Analysis in Several Variables by : Steven G. Krantz
Download or read book Harmonic and Complex Analysis in Several Variables written by Steven G. Krantz and published by Springer. This book was released on 2017-09-20 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
Book Synopsis An Introduction to Complex Function Theory by : Bruce P. Palka
Download or read book An Introduction to Complex Function Theory written by Bruce P. Palka and published by Springer. This book was released on 1990-11-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
Book Synopsis The Prunus mume Genome by : Zhihong Gao
Download or read book The Prunus mume Genome written by Zhihong Gao and published by Springer. This book was released on 2019-07-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the current status of P. mume research, highlighting how the new data coming from the release of the P. mume genomes can advance science and help to solve a number of problems facing the P. mume industry. Prunus mume, which was domesticated in China more than 3,000 years ago as an ornamental plant and for its fruit, is one of the first genomes among the Prunus subfamilies of the Rosaceae family that has been sequenced. Combining the P. mume genome with available data, scientists have succeeded in reconstructing nine ancestral chromosomes of the Rosaceae family, as well as the chromosome fusion, fission and duplication history of three major subfamilies. The P. mume genome sequence adds to our understanding of Rosaceae evolution and provides an important basis for the improvement of fruit trees. This book offers an essential a guide for all those who are interested in gene discovery, comparative genomics, molecular breeding and new breeding techniques; and will be particularly useful for scientists, breeders, university students, and public sector institutes that are involved in the P. mume industry and/or Rosaceae research.
Book Synopsis Complex Systems by : Georgi M. Dimirovski
Download or read book Complex Systems written by Georgi M. Dimirovski and published by Springer. This book was released on 2016-05-19 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a wide-ranging description of the many facets of complex dynamic networks and systems within an infrastructure provided by integrated control and supervision: envisioning, design, experimental exploration, and implementation. The theoretical contributions and the case studies presented can reach control goals beyond those of stabilization and output regulation or even of adaptive control. Reporting on work of the Control of Complex Systems (COSY) research program, Complex Systems follows from and expands upon an earlier collection: Control of Complex Systems by introducing novel theoretical techniques for hard-to-control networks and systems. The major common feature of all the superficially diverse contributions encompassed by this book is that of spotting and exploiting possible areas of mutual reinforcement between control, computing and communications. These help readers to achieve not only robust stable plant system operation but also properties such as collective adaptivity, integrity and survivability at the same time retaining desired performance quality. Applications in the individual chapters are drawn from: • the general implementation of model-based diagnosis and systems engineering in medical technology, in communication, and in power and airport networks; • the creation of biologically inspired control brains and safety-critical human–machine systems, • process-industrial uses; • biped robots; • large space structures and unmanned aerial vehicles; and • precision servomechanisms and other advanced technologies. Complex Systems provides researchers from engineering, applied mathematics and computer science backgrounds with innovative theoretical and practical insights into the state-of-the-art of complex networks and systems research. It employs physical implementations and extensive computer simulations. Graduate students specializing in complex-systems research will also learn much from this collection./pp
