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An Introduction to Difference Equations de Saber Elaydi

An Introduction to Difference Equations

Autor Saber Elaydi
en Limba Engleză Hardback – 29 mar 2005

Cea de-a treia ediție a lucrării An Introduction to Difference Equations reprezintă o revizuire substanțială a textului fundamental semnat de Saber Elaydi, menită să alinieze materialul didactic cu progresele recente din matematica discretă. Putem afirma că principala noutate o constituie introducerea Capitolului 5, o secțiune dedicată integral direcțiilor actuale de cercetare, alături de extinderea demonstrațiilor și aplicațiilor în capitolele de stabilitate. Autorul a integrat rezultate recente privind stabilitatea locală și globală în primele capitole și în anexe, oferind totodată o extensie a Teoremei Hartman–Grobman pentru hărți neinversabile. Structura volumului urmează o progresie riguroasă, pornind de la dinamica ecuațiilor de ordinul întâi și avansând spre sisteme liniare, teoria oscilației și comportament asimptotic, culminând cu aplicații în teoria controlului și fracții continue. Această organizare reflectă expertiza autorului, vizibilă și în alte lucrări coordonate de acesta, precum New Developments in Discrete Dynamical Systems, Difference Equations, and Applications, unde Saber Elaydi explorează frontierele cercetării prezentate la conferințele ICDEA. Considerăm acest volum o alternativă solidă la Difference Equations de Ronald E. Mickens pentru cursurile de analiză matematică, cu avantajul unei abordări mai axate pe dinamica sistemelor și a includerii unor modele biologice complexe, precum modelul larvă-pupă-adult pentru gândacul de făină. În timp ce alte titluri similare, precum Difference Equations and Applications de Youssef N. Raffoul, se concentrează pe stabilitatea exponențială și parametri calitativi, textul lui Elaydi rămâne ancorat în accesibilitatea pedagogică necesară studenților de licență, fără a sacrifica rigoarea matematică a demonstrațiilor.

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Specificații

ISBN-13: 9780387230597
ISBN-10: 0387230599
Pagini: 540
Ilustrații: XXII, 540 p.
Dimensiuni: 167 x 243 x 37 mm
Greutate: 0.97 kg
Ediția:3rd 2005 edition
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Lower undergraduate

De ce să citești această carte

Această ediție este esențială pentru studenții la matematică și inginerie care doresc o introducere clară în ecuațiile cu diferențe. Cititorul câștigă acces la metode moderne de calcul, de la transformata Z la teoria stabilității, explicate prin numeroase grafice și exerciții rezolvate. Este o resursă didactică superioară prin echilibrul dintre teorie și aplicații practice în biologie sau economie.

Descriere scurtă

In contemplating the third edition, I have had multiple objectives to achieve. The ?rst and foremost important objective is to maintain the - cessibility and readability of the book to a broad readership with varying mathematical backgrounds and sophistication. More proofs, more graphs, more explanations, and more applications are provided in this edition. The second objective is to update the contents of the book so that the reader stays abreast of new developments in this vital area of mathematics. Recent results on local and global stability of one-dimensional maps are included in Chapters 1, 4, and Appendices A and C. An extension of the Hartman–Grobman Theorem to noninvertible maps is stated in Appendix D. A whole new section on various notions of the asymptoticity of solutions and a recent extension of Perron’s Second Theorem are added to Chapter 8. In Appendix E a detailed proof of the Levin–May Theorem is presented. In Chapters 4 and 5, the reader will ?nd the latest results on the larval– pupal–adult ?our beetle model. The third and ?nal objective is to better serve the broad readership of this book by including most, but certainly not all, of the research areas in di?erence equations. As more work is being published in the Journal of Di?erence Equations and Applications and elsewhere, it became apparent that a whole chapter needed to be dedicated to this enterprise. With the prodding and encouragement of Gerry Ladas, the new Chapter 5 was born.

Cuprins

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.

Recenzii

Second Edition
S.N. Elaydi
An Introduction to Difference Equations
"The presentation is clear. The book provides numerous interesting applications in various domains (life science, neural networks, feedback control, trade models, heat transfers, etc.) and well-selected exercises with solutions."—AMERICAN MATHEMATICAL SOCIETY
From the reviews of the third edition:
"This is the third edition of a well-established textbook which gives a solid introduction to difference equations suitable for undergraduate students. It covers most aspects from classical results to modern topics. In comparison to the previous edition, more proofs, more detailed explanations, and more applications were added. … Thanks to the many additions, the book stays recent and valuable resource for students and teachers." (G. Teschl, Internationale Mathematische Nachrichten, Issue 202, 2006)
“This book … introduces the concept of difference equations along with several tools, as well as many example applications. … The book … is very enjoyable and smooth to read. … This is an excellent book to keep. It is very good for undergraduate students … . For fresh graduate students, it is good to read … and to keep for future reference. … The book in general is very well written, well organized, contains tons of examples, exercises (with brief solutions) and various applications.” (Adel El-Atawy, SIGACT News, Vol. 40 (3), 2009)

Textul de pe ultima copertă

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

Caracteristici

A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains 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 Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material