Dynamic Equations on Time Scales

An Introduction with Applications

  • Martin Bohner
  • Allan Peterson

Table of contents

  1. Front Matter
    Pages i-x
  2. Martin Bohner, Allan Peterson
    Pages 1-50
  3. Martin Bohner, Allan Peterson
    Pages 51-79
  4. Martin Bohner, Allan Peterson
    Pages 81-134
  5. Martin Bohner, Allan Peterson
    Pages 135-187
  6. Martin Bohner, Allan Peterson
    Pages 189-254
  7. Martin Bohner, Allan Peterson
    Pages 255-287
  8. Martin Bohner, Allan Peterson
    Pages 289-314
  9. Martin Bohner, Allan Peterson
    Pages 315-336
  10. Back Matter
    Pages 337-358

About this book

Introduction

On becoming familiar with difference equations and their close re­ lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro­ duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa­ tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Keywords

Boundary value problem Green's function Transformation calculus difference equations ksa linear algebra linear optimization numerical mathematics ordinary differential equations

Authors and affiliations

  • Martin Bohner
    • 1
  • Allan Peterson
    • 2
  1. 1.Department of MathematicsUniveristy of Missouri-RollaRollaUSA
  2. 2.Department of MathematicsUniversity of NebraskaLincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0201-1
  • Copyright Information Birkhäuser Boston 2001
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6659-4
  • Online ISBN 978-1-4612-0201-1
  • About this book