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Lecture Notes in Mathematics

Asymptotic Integration of Differential and Difference Equations

Authors: Bodine, Sigrun, Lutz, Donald A.

  • 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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eBook $29.99
$69.99 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-3-319-18248-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$89.99 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-18247-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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 self-contained 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 non-experts 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 non-experts interested in the rudiments and applications of this theory.” (Josef Diblík, Mathematical Reviews, May, 2016)

“This book is a self-contained 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

    Bodine, Sigrun (et al.)

    Pages 1-10

  • Asymptotic Integration for Differential Systems

    Bodine, Sigrun (et al.)

    Pages 11-67

  • Asymptotic Representation for Solutions of Difference Systems

    Bodine, Sigrun (et al.)

    Pages 69-117

  • Conditioning Transformations for Differential Systems

    Bodine, Sigrun (et al.)

    Pages 119-177

  • Conditioning Transformations for Difference Systems

    Bodine, Sigrun (et al.)

    Pages 179-208

Buy this book

eBook $29.99
$69.99 (listprice)
price for USA (gross)
valid through June 30, 2017
  • ISBN 978-3-319-18248-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$89.99 (listprice)
price for USA
valid through June 30, 2017
  • ISBN 978-3-319-18247-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Asymptotic Integration of Differential and Difference Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2129
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-18248-3
DOI
10.1007/978-3-319-18248-3
Softcover ISBN
978-3-319-18247-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 402
Topics