β Scribed by Martin Bohner, Allan Peterson
No coin nor oath required. For personal study only.
On becoming familiar with difference equations and their close reΒ 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 introΒ 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 equaΒ 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.
Differential Equations;Applied;Applied;Mathematical Analysis;Mathematics;Science & Math;System Theory;
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An approach to differential equations via exposure to continuous and discrete analysis. Requires only a first semester of calculus and linear algebra. May serve as a reference to stimulate the development of new kinds of equations with new applications.
An approach to differential equations via exposure to continuous and discrete analysis. Requires only a first semester of calculus and linear algebra. May serve as a reference to stimulate the development of new kinds of equations with new applications.
<p><span>This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and
<p><p>This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relat
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1: Conformable Dynamic Calculus on Time Scales -- 1.1 INTRODUCTION -- 1.2 CONFORMABLE DIFFERENTIATION -- 1.3 CONFORMABLE REGRESSIVE FUNCTIONS -- 1.4 THE CONFORMABLE EXPONENTIAL FUNCTION -- 1.5 CONFORMABLE HYPERBOLI