Electronics books often use Laplace to analyze circuits, while in physics we use Fourier, most of the times... if not always: from complex impedances to electromagnetism, quantum mechanics, Green functions, etc etc.
Various sources maintain that Laplace is somehow necessary to properly analyze circuits. I still cannot see why, exactly. Can you point me towards a single well-defined and relevant example/exercise (no generic suggestions like... "stability of amplifiers") that can be solved using Laplace transform and that cannot be solved using Fourier?
Maybe it's me, but I have a hard time in finding examples where Fourier analysis doesn't lead to the same conclusions (of course with some $i\omega$ instead of $s$ in the final equations). Surely in some cases there could be convergence issues maybe, but I think non-converging integrals never scared physicists and most of the times they can be easily tamed in one limit or another.
Note I have nothing against Laplace, I even like it. I am concerned with time investment and homogeneity of mathematical methods.
EDIT. Few examples. In physics one would typically use $Z=1/i\omega C$ for capacitors, not $1/sC$. I could write the response of a RC low pass as $1/(1+i\omega RC)$ using Fourier or $1/(1+sRC)$ using Laplace. I think this applies to any response function. I see Laplace automatically implements initial conditions in linear ODEs but... is there anything different/more insightful with respect to:
Using a characteristic polynomial (in $k$, $s$, $i\omega$, whatever) to find the homogeneous solutions, in case one is interested in transients
Use Fourier to deal with the response function for what concerns the non-homogeneous forcing terms?
Or about stability? But this can be deduced from the location of the poles of the response function, in Fourier just like in Laplace. Pls don't get me wrong here, I am perfectly fine with using Laplace approach. I am just wondering about the practical necessity/advantage of it. This seems just a purely cultural thing, completely replaceable by Fourier analysis. Maybe necessity is there and I don't see it.