Over and Over Again /

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 ove...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Chang, Gengzhe, Sederberg, Thomas W.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Iterative methods (Mathematics)
Transformations (Mathematics)
Itération (Mathématiques)
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Over and Over Again
  • Copyright Page
  • Contents
  • Preface
  • Chapter 1. Transformations and their Iteration
  • Chapter 2. Arithmetic and Geometric Means
  • Chapter 3. Isoperimetric Inequality for Triangles
  • Chapter 4. Isoperimetric Quotient
  • Chapter 5. Colored Marbles
  • Chapter 6. Candy for School Children
  • Chapter 7. Sugar Rather Than Candy
  • Chapter 8. Checkers on a Circle
  • Chapter 9. Decreasing Sets of Positive Integers
  • Chapter 10. Matrix Manipulations
  • Chapter 11. Nested Triangles
  • Chapter 12. Morleyâ€?s Theorem and Napoleonâ€?s TheoremChapter 13. Complex Numbers in Geometry
  • Chapter 14. Birth of an IMO Problem
  • Chapter 15. Barycentric Coordinates
  • Chapter 16. Douglas-Neumann Theorem
  • Chapter 17. Lagrange Interpolation
  • Chapter 18. The Isoperimetric Problem
  • Chapter 19. Formulas for Iterates
  • Chapter 20. Convergent Orbits
  • Chapter 21. Finding Roots by Iteration
  • Chapter 22. Chebyshev Polynomials
  • Chapter 23. Sharkovskiiâ€?s Theorem
  • Chapter 24. Variation Diminishing Matrices
  • Chapter 25. Approximation by Bernstein PolynomialsChapter 26. Properties of Bernstein Polynomials
  • Chapter 27. Bézier Curves
  • Chapter 28. Cubic Interpolatory Splines
  • Chapter 29. Moving Averages
  • Chapter 30. Approximation of Surfaces
  • Chapter 31. Properties of Triangular Patches
  • Chapter 32. Convexity of Patches
  • Appendix A Approximation
  • Appendix B Limits and Continuity
  • Appendix C Convexity
  • Hints and Solutions
  • Bibliography
  • Index

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