EVALUATION OF LINEAR-SYSTEM RESPONSES BY LAPLACE-TRANSFORMATION. CRITICAL REVIEW AND REVISION OF METHOD.

Todate utilization of Laplace-transformation for evaluating linear-system responses, particularly for solving pertinent linear differential equations, is intimately dependent on the so-called initial values included in the derivation theorem. In the present study the origins of inconsistencies are analyzed, the foundations of utilizing Laplace-transformation are reviewed, and the consistent method is developed and justified. The new method takes advantage of the fact that the derivation theorem does not include any initial values, and provides separate solutions to the transmission- and the initial-state problems. The method is consistent with the conventional mathematical theory of differential equations, and is formally identical to that of Fourier-transformation.