Difference Equations
From Rabbits to Chaos
(Sprache: Englisch)
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be...
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Produktinformationen zu „Difference Equations “
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron-Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly.
The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics. TOC:Preface.- Fibonacci Numbers.- Homogeneous Linear Recurrence Relations.- Finite Difference Equations.- Generating Functions.- Nonnegative Difference Equations.- Leslie's Population Matrix Model.- Matrix Difference Equations.- Modular Recurrences.- Computational Complexity.- Some Nonlinear Recurrences.- Appendix A: Worked Examples.- Appendix B: Complex Numbers.- Appendix C: Highlights of Linear Algebra.- Appendix D: Roots in the Unit Circle.- References.- Index.
Klappentext zu „Difference Equations “
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron-Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly.
The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics.
Inhaltsverzeichnis zu „Difference Equations “
Preface Fibonacci Numbers Homogeneous Linear Recurrence Relations Finite Difference Equations Generating Functions Nonnegative Difference Equations Leslie's Population Matrix Model Matrix Difference Equations Modular Recurrences Computational Complexity Some Nonlinear Recurrences Appendix A: Worked Examples Appendix B: Complex Numbers Appendix C: Highlights of Linear Algebra Appendix D: Roots in the Unit Circle References Index
Bibliographische Angaben
- Autoren: Paul Cull , Mary Flahive , Robby Robson
- 2005, 392 Seiten, Maße: 15,6 x 23,7 cm, Kartoniert (TB), Englisch
- Verlag: Springer, New York
- ISBN-10: 0387232346
- ISBN-13: 9780387232348
Sprache:
Englisch
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