How do Electrical Engineering courses in college deal with this? I think differential equations and the Laplace transform is something they learn on the firt semester or year. The dropout rate must be high unless they have found a creative and fun way to teach this stuff.
As an undergrad in EE and CS this was a bit of a mixed experience to me. Laplace transform was presented as kind of a nice hack, but I think the actual development of intuition is delegated to non math specific (engineering) subjects like for instance, Field Theory, Circuit Theory, Signal theory or Numerical methods. It seems that it’s expected that the students just blindly learn the basics of DEs which serve as one of sieves for non-math inclined students (here I may controversially say, rightly so!). You’re simply to swallow bunch of dry scones aka theorems and only then learn how to sue them.
There is zero intuition about the Laplace Transform. It just is. Like English or Chinese.