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Asymptotic Integration of Differential and Difference Equations

  • Sigrun Bodine
  • Donald A. Lutz

Part of the Lecture Notes in Mathematics book series (LNM, volume 2129)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sigrun Bodine, Donald A. Lutz
    Pages 1-10
  3. Sigrun Bodine, Donald A. Lutz
    Pages 11-67
  4. Sigrun Bodine, Donald A. Lutz
    Pages 69-117
  5. Sigrun Bodine, Donald A. Lutz
    Pages 119-177
  6. Sigrun Bodine, Donald A. Lutz
    Pages 179-208
  7. Sigrun Bodine, Donald A. Lutz
    Pages 209-232
  8. Sigrun Bodine, Donald A. Lutz
    Pages 233-236
  9. Sigrun Bodine, Donald A. Lutz
    Pages 237-294
  10. Sigrun Bodine, Donald A. Lutz
    Pages 295-368
  11. Sigrun Bodine, Donald A. Lutz
    Pages 369-391
  12. Back Matter
    Pages 393-404

About this book

Introduction

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. 

Keywords

Asymptotic Behaviour Asymptotic Integration Asymptotic Solutions Difference Equations Linear Differential Equations Perturbations

Authors and affiliations

  • Sigrun Bodine
    • 1
  • Donald A. Lutz
    • 2
  1. 1.Dept. of Mathematics & Computer ScienceUniversity of Puget SoundTacomaUSA
  2. 2.Dept. of Mathematics & StatisticsSan Diego State UniversitySan DiegoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18248-3
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18247-6
  • Online ISBN 978-3-319-18248-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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