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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Colección: | Anneli Lax new mathematical library.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn775429044 | ||
| 003 | OCoLC | ||
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| 049 | |a UAMI | ||
| 245 | 0 | 0 | |a Over and Over Again / |c Gengzhe Chang, Thomas W. Sederberg. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Anneli Lax New Mathematical Library ; |v v. 39 | |
| 500 | |a Title from publishers bibliographic system (viewed on 30 Jan 2012). | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a Chapter 12. Morley�s Theorem and Napoleon�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. Sharkovskii�s Theorem -- Chapter 24. Variation Diminishing Matrices | |
| 505 | 8 | |a 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 | |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Iterative methods (Mathematics) | |
| 650 | 0 | |a Transformations (Mathematics) | |
| 650 | 6 | |a Itération (Mathématiques) | |
| 650 | 7 | |a Iterative methods (Mathematics) |2 fast | |
| 650 | 7 | |a Transformations (Mathematics) |2 fast | |
| 700 | 1 | |a Chang, Gengzhe. | |
| 700 | 1 | |a Sederberg, Thomas W. | |
| 758 | |i has work: |a Over and over again (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGRXyxbwJCgr7QrkYJjYKd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Chang, Gengzhe. |t Over and over Again. |d Washington : Mathematical Association of America, ©2014 |z 9780883856413 |
| 830 | 0 | |a Anneli Lax new mathematical library. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3330418 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL3330418 | ||
| 938 | |a YBP Library Services |b YANK |n 7349815 | ||
| 994 | |a 92 |b IZTAP | ||