OVERVIEW

In most scientific areas the establishment of a useful system model is necessary to describe the system behavior. An effective model need not duplicate the system's physical mechanism, but it is essential that its analysis agree with system measurements to within an acceptable tolerance. For example, the molecules in a lattice structure are to a first approximation represented by masses connected by springs. Obviously this is not the physical arrangement in the solid, but this model has provided useful insights into the system performance, in addition to important results that have been verified by system measurements. Once a suitable model has been established, analyses can replace measurements to determine system behavior.

The linear system has proved to be a useful model for many physical processes. This is fortunate because the principle of superposition applies to these systems, thus allowing general response formulations. The nonlinear system model, however, does not admit of this general response formulation, and analysis is usually confined to specific systems.

Many filtering devices, independent of the hardware realization, are accurately modeled by a linear system. An important member of this class is the system described by an ordinary linear differential equation. So many models are characterized by this differential equation that we may consider this equation as a new model-more precisely, as a mathematical model-with its application in the physical, biological, and social sciences. Consequently its analysis is of theoretic and practical interest.

Here we connect a physical system and the differential equation describing it. We...