EAN: 9781461266594

DYNAMIC EQUATIONS ON TIME SCALES - MARTIN BOHNE...

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.

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