TY - BOOK ID - 77887441 TI - Over and over again AU - Chang, Gengzhe AU - Sederberg, Thomas W PY - 1997 SN - 088385953X 9780883859537 0883856417 9780883856413 PB - [Washington, DC] Mathematical Association of America DB - UniCat KW - Iterative methods (Mathematics) KW - Transformations (Mathematics) KW - Algorithms KW - Differential invariants KW - Geometry, Differential KW - Iteration (Mathematics) KW - Numerical analysis KW - Iterative methods (Mathematics). KW - Transformations (Mathematics). UR - https://www.unicat.be/uniCat?func=search&query=sysid:77887441 AB - 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, Bzier 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. ER -