4.5 Dirac Delta Function

INTRODUCTION

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.

Unit Impulse

Mechanical systems are often acted on by an external force (or emf in an electrical circuit) ...

Get Advanced Engineering Mathematics, 7th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.