1. Review of the Laplace Transform

Our emphasis in this book is on constant parameter linear time invariant dynamic systems. Laplace transform theory is most useful when applied to analysis of linear systems, and this transformation allows the analyst to reduce differential equation problems to algebraic problems. The theory discussed later will be utilized in both the dynamic system analysis and control system design portions of the text. It is demonstrated in this chapter that linear, time-invariant dynamic equations can be transformed into rational functions. Many important input (test) signals can be transformed in this way as well.