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The 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, along with 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. Saber Elaydi is Professor of Mathematics at Trinity University. He is also the author of Discrete Chaos (1999), and the Editor-In-Chief of the Journal of Difference Equations and Applications. About the Second Edition: The book is a valuable reference for anyone who models discrete systems. Dynamicists have the long-awaited discrete counterpart to standard textbooks such as Hirsch and Smale ('Differential Equations, Dynamical Systems, and Linear Algebra'). It is so well written and well designed, and the contents are so interesting to me, that I had a difficult time putting it down. - Shandelle Henson, Journal of Difference Equations and Applications Among the few introductory texts to difference equations this book is one of the very best ones. It has many features that the other texts don't have, e.g., stability theory, the Z-transform method (including a study of Volterra systems), and asymptotic behavior of solutions of difference equations (including Levinson's lemma) are studied extensively. It also contains very nice examples that primarily arise in applications in a variety of disciplines, including neural networks, feedback control, biology, Markov chains, economics, and heat transfer... -Martin Bohner, University of Missouri, Rolla.

Difference equations. --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Difference equations --- Difference equations. --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.

Difference equations. --- Symmetry (Mathematics) --- Integrals. --- Calculus, Integral --- Invariance (Mathematics) --- Group theory --- Automorphisms --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Mathematical analysis --- Inequalities (Mathematics) --- Difference equations --- 51 --- Mathematics --- 51 Mathematics --- Processes, Infinite --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Difference equations.

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This textbook is designed with the needs of today’s student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians. This book is accessible to anyone who has a basic knowledge of precalculus algebra and differential and integral calculus. Its carefully crafted text adopts a concise, simple, no-frills approach to differential equations, which helps students acquire a solid experience in many classical solution techniques. With a lighter accent on the physical interpretation of the results, a more manageable page count than comparable texts, a highly readable style, and over 1000 exercises designed to be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct yet fully rigorous fashion. Apart from several other enhancements, the second edition contains one new chapter on numerical methods of solution. The book formally splits the "pure" and "applied" parts of the contents by placing the discussion of selected mathematical models in separate chapters. At the end of most of the 246 worked examples, the author provides the commands in Mathematica® for verifying the results. The book can be used independently by the average student to learn the fundamentals of the subject, while those interested in pursuing more advanced material can regard it as an easily taken first step on the way to the next level. Additionally, practitioners who encounter differential equations in their professional work will find this text to be a convenient source of reference. Other Springer publications by Christian Constanda: Dude, Can you Count? ISBN: 978-1-84882-538-3; (with D. Doty and W. Hamill) Boundary Integral Equation Methods and Numerical Solutions ISBN: 978-3-319-26307-6; Mathematical Methods for Elastic Plates ISBN: 978-1-4471-6433-3; (with G.R. Thomson) Stationary Oscillations of Elastic Plates ISBN: 978-0-8176-8340-8. Christian Constanda, MS, PhD, DSc, is the holder of the Charles W. Oliphant Endowed Chair in Mathematical Sciences at the University of Tulsa, USA. He is also the Chairman of the International Consortium on Integral Methods in Science and Engineering (IMSE).

Mathematics. --- Difference equations. --- Functional equations. --- Difference and Functional Equations. --- Equations, Functional --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Functional analysis