Asymptotic Integration of Differential and Difference Equations
Authors: Bodine, Sigrun, Lutz, Donald A.
Free Preview Contains a wealth of results both for differential as well as difference equations
 Illuminates new approaches and suggests new directions of inquiry
 Includes a treatment of dynamic equations on time scales
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 About this book

This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations.
After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales.
Asymptotic Integration of Differential and Difference Equations is a selfcontained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to nonexperts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
 Reviews

“This very readable book gives a nice presentation of the theory of asymptotic integration for both linear differential and linear difference equations … . The book provides a very deep insight into the theory of asymptotic integrations of linear differential and difference equations. Excellently written, it has a place in the bookcase of every mathematician, engineer or student, and is also of value for nonexperts interested in the rudiments and applications of this theory.” (Josef Diblík, Mathematical Reviews, May, 2016)
“This book is a selfcontained and clearly structured presentation of important results in asymptotic integration and the techniques which are used in this field. I have really enjoyed reading it. This text appeals to (non)experts who are interested in asymptotic behavior of solutions to differential and difference equations. It can be of interest to students in mathematics, applied sciences, and engineering. For anyone who works in asymptotic integration, this monograph is a must.” (Pavel Rehak, zbMATH 1331.34001, 2016)
 Table of contents (10 chapters)


Introduction, Notation, and Background
Pages 110

Asymptotic Integration for Differential Systems
Pages 1167

Asymptotic Representation for Solutions of Difference Systems
Pages 69117

Conditioning Transformations for Differential Systems
Pages 119177

Conditioning Transformations for Difference Systems
Pages 179208

Table of contents (10 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Asymptotic Integration of Differential and Difference Equations
 Authors

 Sigrun Bodine
 Donald A. Lutz
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 2129
 Copyright
 2015
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing Switzerland
 eBook ISBN
 9783319182483
 DOI
 10.1007/9783319182483
 Softcover ISBN
 9783319182476
 Series ISSN
 00758434
 Edition Number
 1
 Number of Pages
 XI, 402
 Topics