Especially for 2nd & 3rd year courses I'm looking at such as PDEs, fourier series & laplace tranforms, Vector calculus, intermediate level linear algebra, computational maths, lagranian and hamiltonian dynamics?
I imagine the courses you listed would have little proofs as they rely a lot on Calculus for which you've seen the proofs already. As a physics major, I recall taking these courses and not having to do any proofs. You could check with the profs of these classes and see what they say or the course catalog and see if its for engineering and science majors too that would be a clue.
I think "intermediate" linear algebra sounds like it might be a little proofy. Others would depend on the particular class. Best way to find out would be to e-mail or talk to the instructor because it's up to them how they structure the class.