Dynamic Equations on Time Scales

1. Front Matter

   Pages i-x

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2. The Time Scales Calculus

   • Martin Bohner, Allan Peterson

   Pages 1-50

3. First Order Linear Equations

   • Martin Bohner, Allan Peterson

   Pages 51-79

4. Second Order Linear Equations

   • Martin Bohner, Allan Peterson

   Pages 81-134

5. Self-Adjoint Equations

   • Martin Bohner, Allan Peterson

   Pages 135-187

6. Linear Systems and Higher Order Equations

   • Martin Bohner, Allan Peterson

   Pages 189-254

7. Dynamic Inequalities

   • Martin Bohner, Allan Peterson

   Pages 255-287

8. Linear Symplectic Dynamic Systems

   • Martin Bohner, Allan Peterson

   Pages 289-314

9. Extensions

   • Martin Bohner, Allan Peterson

   Pages 315-336

10. Back Matter

    Pages 337-358

    PDF

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.

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

"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

• Department of Mathematics, Univeristy of Missouri-Rolla, Rolla, USA

  Martin Bohner

• Department of Mathematics, University of Nebraska, Lincoln, USA

  Allan Peterson

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