4.5 Dirac Delta Function
Just before the Remarks on page 229, we indicated that as an immediate consequence of Theorem 4.2.3, F(s) = 1 cannot be the Laplace transform of a function f that is piecewise continuous on [0, ∞) and of exponential order. In the discussion that follows we are going to introduce a function that is very different from the kinds that you have studied in previous courses. We shall see that there does indeed exist a function, or more precisely a generalized function, whose Laplace transform is F(s) = 1.
Mechanical systems are often acted on by an external force (or emf in an electrical circuit) ...
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