An Introduction to Difference Equations
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ISBN-13:
9781441920010
Veröffentl:
2010
Erscheinungsdatum:
01.12.2010
Seiten:
540
Autor:
Saber Elaydi
Gewicht:
782 g
Format:
241x159x38 mm
Sprache:
Englisch
Beschreibung:
A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamicsContains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations.Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems.Includes chapters on continued fractions, orthogonal polynomials and asymptotics.Lucid and transparent writing style
This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, and also recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model.
* Preface * List of Symbols * Dynamics of First-Order Difference Equations * Linear Difference Equations of Higher Order * Systems of Linear Difference Equations * Stability Theory * Higher Order Scalar Difference Equations * The Z-Transform Method and Volterra Difference Equations * Oscillation Theory * Asymptotic Behavior of Difference Equations * Applications to Continued Fractions and Orthogonal Polynomials * Control Theory * Answers and Hints to Selected Problems * Appendix A: Stability of Nonhyperbolic Fixed Points of Maps on the Real Line * Vandermonde Matrix * Stability of Nondifferentiable Maps * Stable Manifold and Hartman-Grobman-Cushing Theorems * Levin-May Theorem * Classical Orthogonal Polynomials * Identities and Formulas * References * Index
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