題組內容

1. Function f(t) is defined for positive values of t. The Laplace transform of f(t), denoted as L{f(t)}, is defined as:

That is, after the transform, f(t) becomes a new function F which is a function of variable s.

1.2 (4%) Let √(df(t)/dt) be denoted as f'(t). Then show that L{f'(t)} = sF(s)-f(0). You may need to apply integration by parts for the calculation.