I recently have started learning Laplace transforms, it seems like its just a bunch of looking up tables. Along with having a bunch of standard Laplace transforms memorized. Is this how it usually is when dealing with transforms for the first time? I feel like I am not really even doing math, its almost like a bunch of fitting to known equations.
Haven't you learned what is the definition of the Laplace transform? That is how you can work them out for unknown functions. But in practice you learn the common ones, just like you learn that ##d(\sin x)/dx = \cos x##, and look up others in tables. But the interesting thing about Laplace transforms is what you can do with them, not how to calculate them. Maybe your course hasn't got to that yet.