Basic Calculus on Time Scales and Some of Its Applications
The study of dynamic systems on time scales not only unifies continuous and discrete processes, but also helps in revealing diversities in the corresponding results. In this paper we shall develop basic tools of calculus on time scales such as versions of Taylor's formula, l'Hôspital's rule, and Kneser's theorem. Applications of these results in the study of asymptotic and oscillatory behavior of solutions of higher order equations on time scales are addressed. As a further application of Taylor's formula, Abel-Gontscharoff interpolating polynomial on time scales is constructed and best possible error bounds are offered. We have also included notes at the end of each section which indicate further scope of the calculus developed in this paper.
M. Bohner and R. P. Agarwal, "Basic Calculus on Time Scales and Some of Its Applications," Results in Mathematics, Springer Verlag, Jan 1999.
The definitive version is available at http://dx.doi.org/10.1007/BF03322019
Mathematics and Statistics
Keywords and Phrases
time scales; Taylor's theorem; l'Hôspital's rule; kneeser's Theorem; Abel-Gontscharoff interpolation
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