This book covers the basic elements of difference equations and the
tools of difference and sum calculus necessary for studying and solv-
ing, primarily, ordinary linear difference equations. Examples from
various fields are presented clearly in the first chapter, then
discussed along with their detailed solutions in Chapters 2-7. The book
is in- tended mainly as a text for the beginning undergraduate course in
difference equations, where the "operational sum calculus" of the di-
rect use of the discrete Fourier transforms for solving boundary value
problems associated with difference equations represents an added new
feature compared to other existing books on the subject at this
introductory level. This means that in addition to the familiar meth-
ods of solving difference equations that are covered in Chapter 3, this
book emphasizes the use of discrete transforms. It is an attempt to
introduce the methods and mechanics of discrete transforms for solv- ing
ordinary difference equations. The treatment closely parallels what many
students have already learned about using the opera- tional (integral)
calculus of Laplace and Fourier transforms to solve differential
equations. As in the continuous case, discrete operational methods may
not solve problems that are intractable by other meth- ods, but they can
facilitate the solution of a large class of discrete initial and
boundary value problems. Such operational methods, or what we shall term
"operational sum calculus," may be extended eas- ily to solve partial
difference equations associated with initial and/or boundary value
problems.
