Dynamic Equations on Time Scales

An Introduction with Applications

Authors: Bohner, Martin, Peterson, Allan

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About this Textbook

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.

Reviews

"This would be an excellent book to use in a topics course on dynamic equations on time scales at the advanced undergraduate level and/or beginning graduate level."

—Zentralblatt Math

"The monograph under review comes at an excellent time in the rapid development of dynamic equations on time scales. Both authors are authorities in this field of study and they have produced an excellent introduction to it. Much of the material is accessible to upper-level undergraduate mathematics majors, and yet, the results and the techniques are pertinent to active researchers in the area."

—Mathematical Reviews


Table of contents (8 chapters)

  • The Time Scales Calculus

    Bohner, Martin (et al.)

    Pages 1-50

  • First Order Linear Equations

    Bohner, Martin (et al.)

    Pages 51-79

  • Second Order Linear Equations

    Bohner, Martin (et al.)

    Pages 81-134

  • Self-Adjoint Equations

    Bohner, Martin (et al.)

    Pages 135-187

  • Linear Systems and Higher Order Equations

    Bohner, Martin (et al.)

    Pages 189-254

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4612-0201-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-0-8176-4225-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4612-6659-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Dynamic Equations on Time Scales
Book Subtitle
An Introduction with Applications
Authors
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0201-1
DOI
10.1007/978-1-4612-0201-1
Hardcover ISBN
978-0-8176-4225-9
Softcover ISBN
978-1-4612-6659-4
Edition Number
1
Number of Pages
X, 358
Topics