The right use of the Laplace transform in circuits

It is shown that in using the Laplace transform one has to start with null initial conditions in order to avoid errors in the derivative and integral operations. In that case the matrix representation of the circuits using the Laplace transform becomes possible and the resolution of integral-differential equations is straightforward. Nevertheless, it is possible to use the Laplace transform with signals that have no null initial conditions, keeping the mathematical coherence, by choosing between two ways: (1) shifting the origin of time domains to the left to obtain the null initial conditions, and (2) using the superposition theorem to obtain one partial signal with null initial conditions