This is the first time I've ever needed to use Green's functions while solving problems, although I've used the delta input in differential equations before to solve for systems with an 'impulse'. I am still trying to work my way around them and wanted to know how important they were. I've used the Laplace Transform plenty of times before and am comfortable with it. I can solve the problems that I am presented with (Simple Harmonic Oscillators; Damped, undamped etc) far quicker using the method of the Laplace transform. Would you guys recommend putting Green's functions away for later, or should I begin acquainting myself with these functions right from the start? Are they all that important? Why couldn't I just stick with the LT?