[julie_m]

It's not as though the maths is impossible..... Just hard work. Any circuit of resistors, capacitors and inductors can be modelled with a system of differential equations. But you don't even have to solve them the hard way! Using a computer, it's simple enough to run a numerical approximation, setting δt as small as you like, doing the calculations over and over again and adding up all the δV's and δI's; and then plot a graph to show what is happening over time. Basically it's like counting the squares on graph paper to get the area under a curve, as a way to an approximate solution to a differential equation; only with the computer doing all the work.