INCONSISTENT INITIAL CONDITIONS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 102

Also because

we arrive at

These results indicate that the existence of the impulsive component at
switching instants can be sensed by monitoring the integral

The integral is nonzero if contains a Dirac impulse at and zero,
otherwise. In what follows we show how (5.59) is evaluated numerically.

6.1 Dirac Impulses in Linear Circuits
For linear circuits, the integration of (5.59) can be evaluated conve-
niently using numerical Laplace inversion.
Notice that

we have

is thus obtained by first integrating from to and

then from to