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Zeros Of Sections Of Power Series

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Zeros of Sections of Power Series

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Zeros of Sections of Power Series by A. Edrei,E. B. Saff,R. S. Varga Book Summary:

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Analytic Theory of Polynomials

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Analytic Theory of Polynomials by Qazi Ibadur Rahman,Gerhard Schmeisser Book Summary:

'A nicely written book that will be useful for scientists, engineers and mathematicians from other fields. It can be strongly recommended as an undergraduate or graduate text and as a comprehensive source for self study.' -EMSPresents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.

Entire Functions and Related Parts of Analysis

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Entire Functions and Related Parts of Analysis by Jacob Korevaar,American Mathematical Society Book Summary:

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Abstracts of Dissertations for the Degrees of Doctor of Philosophy and Doctor of Education, with the Titles of Theses Accepted for the Degrees of Engineer, Master of Arts, and Master of Science

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Abstracts of Dissertations for the Degrees of Doctor of Philosophy and Doctor of Education, with the Titles of Theses Accepted for the Degrees of Engineer, Master of Arts, and Master of Science by Stanford University Book Summary:

Download or read Abstracts of Dissertations for the Degrees of Doctor of Philosophy and Doctor of Education, with the Titles of Theses Accepted for the Degrees of Engineer, Master of Arts, and Master of Science book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Zeros of Gaussian Analytic Functions and Determinantal Point Processes

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Zeros of Gaussian Analytic Functions and Determinantal Point Processes by John Ben Hough,Manjunath Krishnapur ,Yuval Peres ,B\'alint Vir\'ag Book Summary:

The book examines in some depth two important classes of point processes, determinantal processes and ``Gaussian zeros'', i.e., zeros of random analytic functions with Gaussian coefficients. These processes share a property of ``point-repulsion'', where distinct points are less likely to fall close to each other than in processes, such as the Poisson process, that arise from independent sampling. Nevertheless, the treatment in the book emphasizes the use of independence: for random power series, the independence of coefficients is key; for determinantal processes, the number of points in a domain is a sum of independent indicators, and this yields a satisfying explanation of the central limit theorem (CLT) for this point count. Another unifying theme of the book is invariance of considered point processes under natural transformation groups. The book strives for balance between general theory and concrete examples. On the one hand, it presents a primer on modern techniques on the interface of probability and analysis. On the other hand, a wealth of determinantal processes of intrinsic interest are analyzed; these arise from random spanning trees and eigenvalues of random matrices, as well as from special power series with determinantal zeros. The material in the book formed the basis of a graduate course given at the IAS-Park City Summer School in 2007; the only background knowledge assumed can be acquired in first-year graduate courses in analysis and probability.

Value Distribution Theory and Its Applications

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Value Distribution Theory and Its Applications by Chung-Chun Yang,Special Session on Value Distribution Theory and Its Applications Book Summary:

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Transcendental Representations with Applications to Solids and Fluids

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Transcendental Representations with Applications to Solids and Fluids by Luis Manuel Braga da Costa Campos Book Summary:

Building on the author’s previous book in the series, Complex Analysis with Applications to Flows and Fields (CRC Press, 2010), Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. This book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible irrotational flows, unsteady flows, rotating flows, surface tension and capillarity, deflection of membranes under load, torsion of rods by torques, plane elasticity, and plane viscous flows. The two books together offer a complete treatment of complex analysis, showing how the elementary transcendental functions and other complex functions are applied to fluid and solid media and force fields mainly in two dimensions. The mathematical developments appear in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. The last chapter presents a set of detailed examples. Each chapter begins with an introduction and concludes with related topics. Written by one of the foremost authorities in aeronautical/aerospace engineering, this self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.

Mathematical Reviews

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Mathematical Reviews by N.A Book Summary:

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Applied and Computational Complex Analysis, Volume 1

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Applied and Computational Complex Analysis, Volume 1 by Peter Henrici Book Summary:

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Sequences of Polynomials

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Sequences of Polynomials by Paul Rosenbloom Book Summary:

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Complex Analysis

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Complex Analysis by Jane P. Gilman,Irwin Kra,Rubi E. Rodriguez,Rub E Rodr Guez Book Summary:

Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.

Ordinary Differential Equations

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Ordinary Differential Equations by Vladimir I. Arnold Book Summary:

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW

An Atlas of Functions

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An Atlas of Functions by Keith B. Oldham,Jan Myland,Jerome Spanier Book Summary:

This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

The Observatory

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The Observatory by N.A Book Summary:

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Classical Complex Analysis

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Classical Complex Analysis by I-Hsiung Lin Book Summary:

Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.

Complex Analysis

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Complex Analysis by Rubí E. Rodríguez,Irwin Kra,Jane P. Gilman Book Summary:

The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Structured Matrices and Polynomials

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Structured Matrices and Polynomials by Victor Pan Book Summary:

Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.

Computer Evaluation of Mathematical Functions

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Computer Evaluation of Mathematical Functions by C. T. Fike Book Summary:

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