TABLE OF CONTENTS This appendix is a treatment of linear difference equations with constant coefficients and it is confined to first and secondorder difference equations and their solution. Higherorder difference equations of this type and their solution is facilitated with the 
-transform. [*]
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 [ ] for solving nonlinear equations. While recursive methods yield a desired result, they do not provide a closedf orm solution. If a closedform 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.
[*] For an introduction and applications of the -transform please refer to Signals and Systems with MATLAB Computing and Simulink Modeling, Third Edition, ISBN 0-9744239-9-8.
[ ] Newton s method is discussed in Chapter 2 .
A secondorder difference equation has the form
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 outputs y(n ? 1)...
