ABSTRACT
The success of transformation techniques in solving initial value problems and other applications hinges on their operational properties. Rules that govern how operations in the time domain translate to operations in their transformation images are called operational laws or rules. The chapter presents the 10 basic rules that are useful in applications of the Laplace transformation to differential equations. Keep in mind that people ultimate goal is to solve differential equations with possible piecewise continuous forcing functions. Utilization of the Laplace transformation in differential equations involves two steps: the direct Laplace transform and the inverse Laplace transform. Mechanical systems are also often driven by an external force of large magnitude that acts for only very short periods of time. The Dirac delta-function has numerous applications in theoretical physics, mathematics, and engineering problems. In electric circuits, the delta-function can serve as a model for voltage spikes.
