Simon, an extremely useful and valuable book for electronics students and engineers is this one (I still use my copy from the 80s, it's become somewhat tattered over the years):
"Mathematical Handbook of Formulas and Tables",
Murray R. Spiegel,
Schaum's Outline Series.
It contains all formulas that you'll ever need. But more importantly, it's got tables of the inverse Laplace transforms.
As you've gathered from the replies above, finding the equations for a circuit using Laplace notation is not difficult. Finding a transfer function from those is also not difficult. And doing a frequency analysis (amplitude, phase etc.) is also not difficult.
But getting back in the time domain can be really hard, eg, for impulse response, ringing, rise time, overshoot etc., because this is where you need the inverse Laplace.
If you don't have it, I encourage you to get it. Cheers.