ENGLISH

Polynomials and Polynomial Inequalities

By Peter Borwein , Tamás Erdélyi (auth.)

Book information

Publisher
Springer-Verlag New York
Year
1995
ISBN
0387945091, 9780387945095
DOI
10.1007/978-1-4612-0793-1
LCC
QA241 .B775 1995
Open Library ID
OL1276729M
Language
english
Format
DJVU
Filesize
2 MB (2523432 bytes)
Series
Graduate Texts in Mathematics 161
Edition
1
Pages
480\486
Library
Kolxo3
DPI
600
Time added
2011-06-04 13:46:07
Analysis; Algebra

Description

Polynomials pervade mathematics, virtually every branch of mathematics from algebraic number theory and algebraic geometry to applied analysis and computer science, has a corpus of theory arising from polynomials. The material explored in this book primarily concerns polynomials as they arise in analysis; it focuses on polynomials and rational functions of a single variable. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis. 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 conclude the book.

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