International Journal of Innovative Technology and Research
Abstract
A goal of science is to develop the means for reliable prediction to guidedecision and action. This is accomplished by finding algorithmiccompressions of observations and physical laws. Physical laws arestatements about classes of phenomena, and initial conditions are statementsabout particular systems. Thus, it is the solutions to the equations, and notthe equations themselves, that provide a mathematical description of thephysical phenomena. In constructing and refining mathematical theories, werely heavily on models. At its conception, a model provides the frameworkfor a mathematical interpretation of new phenomena. We apply linearity when we model the behaviour of a device or system that is forced or pushed by a complex set of inputs or excitations. We obtain the response of that device or system to the sum of the individual inputs by adding or superposing the separate responses of the system to each individual input. This important result is called the principle of superposition. Engineers use this principle to predict the response of a system to a complicated input by decomposing or breaking down that input into a set of simpler inputs that produce known system responses or behaviour
