# Problems solving in electrical engineering – Table of the main inverse Laplace transformations (transition to the time function)

The second stage of the calculation of transient processes by the operator method is the transition from image to a time function. This operation can be done by various methods.

The first method is to use the formulas of correspondence between the functions of the operator p (image space) and the functions t (space-time). Part of the formulas, the most commonly used in practice is shown in the table below. In the scientific literature there are some studies that contain a large number of correspondence formulas covering almost all practical problems. It is better to use transition table if there is among the roots of the equation multiple roots.

The second method is to apply the expansion formula.

The third method is a direct application of the formula of the inverse Laplace transformation using the theory of residues.