The field of application of difference equations is very wide, especially in the modeling of phenomena, which increasingly are being considered discrete. Thus, instead of the usual formulation in terms of differential equations, one encounters difference equations. In many cases a formulation using a discrete independent variable will suffice, but this severely restricts the available solution procedures. Further, it is often desirable to embed the original formulation into the wider class of difference equations with analytic independent variable, which not only enlarges the class of solution procedures but opens the way to answering questions concerning sensitivity, that is, to differentiation and to wider methods of approximation.
The author, throughout his working career, has served in the capacity of mathematical consultant. The problems brought to him were of a varied nature, drawn from engineering, communication, physics, information theory, and astronomy; he was expected to use his mathematical knowledge to produce practically relevant and usable results. The mathematical tools that were employed included differential equations.Volterra integral equations, probability theory, and, especially, difference equations. The techniques introduced in this book were particularly useful in the construction of approximations and solutions for many of the practical problems with which he dealt.