ABSTRACT
This chapter considers some of the properties of linear systems. These properties, which are simplifying assumptions with regard to real-world systems and especially with respect to human performance, are nonetheless very useful assumptions in many instances. The assumption of linearity will greatly facilitate the ability to manipulate block diagrams and differential equations. Differential equations are critical analytic tools for deriving the response of dynamic systems. Laplace transforms are tools that make it easier to manipulate and solve linear differential equations. Block diagrams are important conventions for visualizing the structure of dynamic systems. For linear systems, the operation of convolution allows an analytical calculation of the behavior of a system from knowledge of the inputs and the system dynamics. Convolution in the time domain can be accomplished by multiplication of the Laplace transforms of the input and the impulse response. The Laplace transform permits using knowledge of algebra to solve differential and integral equations.
