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.
Polynomials and Polynomial Inequalities
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"This is a wonderful book which is strongly recommended for use in a class with students who are willing to work on the proofs, rather than to digest fully prepared and worked out proofs and examples." Jnl of Approximation Theory
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Inside This Book
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First Sentence:
The focus for this book is the polynomial of a single variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
distinct nonnegative real numbers, gap condition inf, dyn dxn, distinct positive real numbers, constrained polynomials, extremal polynomials, orthonormal collection, nonnegative polynomials, alternation points, distinct positive numbers, alternation sequence, nonnegative nondecreasing function, uniform closure, best uniform approximation, distinct real numbers, internal zero, orthonormal polynomials, open unit disk, distinct zeros, lead coefficient, generalized polynomials, nonnegative coefficients, distinct complex numbers, classical inequalities, trigonometric polynomials Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mean Value Theorem, Fundamental Theorem of Algebra, Prove Corollary, Generating Function, Proof of Corollaries New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The focus for this book is the polynomial of a single variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
distinct nonnegative real numbers, gap condition inf, dyn dxn, distinct positive real numbers, constrained polynomials, extremal polynomials, orthonormal collection, nonnegative polynomials, alternation points, distinct positive numbers, alternation sequence, nonnegative nondecreasing function, uniform closure, best uniform approximation, distinct real numbers, internal zero, orthonormal polynomials, open unit disk, distinct zeros, lead coefficient, generalized polynomials, nonnegative coefficients, distinct complex numbers, classical inequalities, trigonometric polynomials Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mean Value Theorem, Fundamental Theorem of Algebra, Prove Corollary, Generating Function, Proof of Corollaries New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Bernstein Polynomials (AMS Chelsea Publishing) by G. G. Lorentz on page 164, and Back Matter
- Approximation Theory (Pure and Applied Mathematics) (Chapman & Hall/CRC Pure and Applied Mathematics) by Narenda Govil in Back Matter (1), and Back Matter (2)
- Complex Analysis by Lars Ahlfors on page 14, and Back Matter
- Nonlinear Approximation Theory (Springer Series in Computational Mathematics) by Dietrich Braess on page 288, and Back Matter
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- Approximation Theory (Pure and Applied Mathematics) (Chapman & Hall/CRC Pure and Applied Mathematics) by Narenda Govil on page 95, and page 129
- A Panorama of Hungarian Mathematics in the Twentieth Century, I (Bolyai Society Mathematical Studies) (v. 1) by Janos Horvath on page 151, and Back Matter
- Computational Excursions in Analysis and Number Theory by Peter Borwein on page 9, and Back Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Back Matter
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Front Matter
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