Over and over again / / by Gengzhe Chang and Thomas W. Sederberg

• Autore: Chang Gengzhe
• Pubblicazione: Washington, DC, : Mathematical Association of America, 1997
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (xiv, 309 pages) : digital, PDF file(s)
• Disciplina: 511.4
• Soggetto topico: Iterative methods (Mathematics); Transformations (Mathematics)
• Altri autori: SederbergThomas W
• Note generali: Title from publisher's bibliographic system (viewed on 02 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Transformations and their iteration -- Arithmetic and geometric means -- Isoperimetric inequality for triangles -- Isoperimetric quotient -- Colored marbles -- Candy for school children -- Sugar rather than candy -- Checkers on a circle -- Decreasing sets of positive integers -- Matrix manipulations -- Nested traingles -- Morley's theorem and Napoleon's theorem -- Complex numbers in geometry -- Birth of an IMO problem -- Barycentric coordinates -- Douglas-Neumann theorem -- Lagrange interpolation -- The Isoperimetric problem -- Formulas for iterates -- Convergent orbits -- Finding roots by iteration -- Chebyshev polynomials -- Sharkovskii's theorem -- Variation diminishing matrices -- Approximation by Bernstein polynomials -- Properties of Bernstein polynomials -- Bézier curves -- Cubic interpolatory splines -- Moving averages -- Approximation of surfaces -- Properties of triangular patches -- Convexity of patches.
• Sommario/riassunto: 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.
• Titolo autorizzato: Over and over again
• ISBN: 0-88385-953-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910821724303321
• Lo trovi qui: Univ. Federico II