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Covers its topic in greater depth than the typical standard books on polynomial algebra
Book Synopsis Polynomials by : Victor V. Prasolov
Download or read book Polynomials written by Victor V. Prasolov and published by Springer Science & Business Media. This book was released on 2009-09-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers its topic in greater depth than the typical standard books on polynomial algebra
Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Book Synopsis Analytic Theory of Polynomials by : Qazi Ibadur Rahman
Download or read book Analytic Theory of Polynomials written by Qazi Ibadur Rahman and published by Oxford University Press. This book was released on 2002 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
Book Synopsis Positive Polynomials by : Alexander Prestel
Download or read book Positive Polynomials written by Alexander Prestel and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.
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.
Book Synopsis Interpolation and Approximation by Polynomials by : George M. Phillips
Download or read book Interpolation and Approximation by Polynomials written by George M. Phillips and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.
Book Synopsis Polynomials by : Cheon Seoung Ryoo
Download or read book Polynomials written by Cheon Seoung Ryoo and published by BoD – Books on Demand. This book was released on 2019-05-02 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
"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"--
Book Synopsis An Introduction to Orthogonal Polynomials by : Theodore S Chihara
Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2011-02-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
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.
Book Synopsis Polynomials and Polynomial Inequalities by : Peter Borwein
Download or read book Polynomials and Polynomial Inequalities written by Peter Borwein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
Book Synopsis Geometry of Polynomials by : Morris Marden
Download or read book Geometry of Polynomials written by Morris Marden and published by American Mathematical Soc.. This book was released on 1949-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
This book is the definitive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener-Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis.
Book Synopsis Matrix Polynomials by : I. Gohberg
Download or read book Matrix Polynomials written by I. Gohberg and published by SIAM. This book was released on 2009-07-23 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener-Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis.
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Book Synopsis Orthogonal Polynomials by : Gabor Szeg
Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
