Difference Equations

From Rabbits to Chaos

Paul Cull, Mary Flahive, Robert Robson - Collection Undergraduate Texts in Mathematics

392 pages, parution le 31/01/2005

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Résumé

Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers.

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.

L'auteur - Paul Cull

Paul Cull is a professor of Computer Science at Oregon State University.

L'auteur - Mary Flahive

Mary Flahive is a professor of Mathematics at Oregon State University.

L'auteur - Robert Robson

Robby Robson is president of Eduworks, an e-learning consulting firm.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Paul Cull, Mary Flahive, Robert Robson
Collection	Undergraduate Texts in Mathematics
Parution	31/01/2005
Nb. de pages	392
Format	16 x 24
Couverture	Relié
Poids	687g
Intérieur	Noir et Blanc
EAN13	9780387232331
ISBN13	978-0-387-23233-1