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Over and over again
Authors: ---
ISBN: 0883856417 Year: 1997 Publisher: New York (N.Y.) : Mathematical association of America,

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Over and over again
Authors: --- --- ---
ISBN: 088385953X 9780883859537 0883856417 9780883856413 Year: 1997 Publisher: Washington, DC : Mathematical Association of America,

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Abstract

Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, BŽzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computer-aided geometric design.

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