Polynomials

Polynomials
Title Polynomials PDF eBook
Author E.J. Barbeau
Publisher Springer Science & Business Media
Pages 484
Release 2003-10-09
Genre Mathematics
ISBN 9780387406275

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The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.

Interpolation and Approximation by Polynomials

Interpolation and Approximation by Polynomials
Title Interpolation and Approximation by Polynomials PDF eBook
Author George M. Phillips
Publisher Springer Science & Business Media
Pages 325
Release 2006-04-06
Genre Mathematics
ISBN 0387216820

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In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Polynomials

Polynomials
Title Polynomials PDF eBook
Author Cheon Seoung Ryoo
Publisher BoD – Books on Demand
Pages 174
Release 2019-05-02
Genre Mathematics
ISBN 183880269X

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Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Polynomials

Polynomials
Title Polynomials PDF eBook
Author Victor V. Prasolov
Publisher Springer Science & Business Media
Pages 311
Release 2009-09-23
Genre Mathematics
ISBN 3642039804

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Covers its topic in greater depth than the typical standard books on polynomial algebra

Polynomials and Polynomial Inequalities

Polynomials and Polynomial Inequalities
Title Polynomials and Polynomial Inequalities PDF eBook
Author Peter Borwein
Publisher Springer Science & Business Media
Pages 508
Release 1995-09-27
Genre Mathematics
ISBN 9780387945095

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After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality round off the text. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.

An Introduction to Orthogonal Polynomials

An Introduction to Orthogonal Polynomials
Title An Introduction to Orthogonal Polynomials PDF eBook
Author Theodore S Chihara
Publisher Courier Corporation
Pages 276
Release 2011-02-17
Genre Mathematics
ISBN 0486479293

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"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--

Analytic Theory of Polynomials

Analytic Theory of Polynomials
Title Analytic Theory of Polynomials PDF eBook
Author Qazi Ibadur Rahman
Publisher Oxford University Press
Pages 760
Release 2002
Genre Language Arts & Disciplines
ISBN 9780198534938

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Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications