I don't understand why the laplace transform of some function, say f(t), has to be "piecewise continuous" and not "continuous". Is "piecewise continuous" sort of like the minimum requirement? This troubles me because I don't think f(t)=t is piecewise continuous, it's simply continuous...
Also, I don't understand what's so special about a function being of "exponential order". Can someone explain to me why this property is so special and apparently makes the Laplace Transform exist?
Also, my teacher says that f(t) has to be of exponential order from [0,infinity] and other sources say that it at least has to be of exponential order from [T,infinity] where T>0.