TABLE OF CONTENTS This appendix is a treatment of linear difference equations with constant coefficients and it is confined to first- and second-order difference equations and their solution. Higher-order difference equations of this type and their solution is facilitated with the 
-transform [1].
In mathematics, a recursion is an expression, such as a polynomial, each term of which is determined by application of a formula to preceding terms. The solution of a difference equation is often obtained by recursive methods. An example of a recursive method is Newton's method [2] for solving non-linear equations. While recursive methods yield a desired result, they do not provide a closed-form solution. If a closed-form solution is desired, we can solve difference equations using the Method of Undetermined Coefficients, and this method is similar to the classical method of solving linear differential equations with constant coefficients. This method is described in the next section.
[1] For an introduction and applications of the 
-transform please refer to Signals and Systems with MATLAB Applications, ISBN 0-9709511 -6-7.
[2] For a complete discussion of Newton's Method, please refer to Numerical Analysis Using MATLAB and Spreadsheets , ISBN 0-9709511-1-6.
A second-order difference equation has the form
| (B.1) |  |
where a 1 and a 2 are constants and the right side is some function of n. This difference equation expresses the output y(n) at time n as the linear combination of two previous...
