Difference Equations: Theory, Applications And Advanced Topics, Third Edition (chapman & Hall/crc Monographs And Research Notes In Mathematics)
Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations nonlinear equations that may be reduced to linear equations and partial difference equations. New to the Third Edition * New chapter on special topics, including discrete Cauchy-Euler equations gamma, beta, and digamma functions Lambert W-function Euler polynomials functional equations and exact discretizations of differential equations * New chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences * Additional problems in all chapters * Expanded bibliography to include recently published texts related to the subject of difference equations Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanationsThis book covers many important classes of difference equations, including general, linear, first, second, and Nth order, along with nonlinear equations, partial difference equations, functional equations, and Nth order equations having constant coefficients. It presents a wide range of techniques for calculating exact and approximate solutions. Numerous worked examples illustrate the use of the methodologies. This edition includes new chapters on advanced topics, such as asymptotic behavior of solutions and functional equations, as well as problems that have appeared in the recent mathematical literature.