Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition

Appendix D

Laplace Transforms

We have had several occasions to use Laplace transforms in this text. This appendix examines useful properties of the Laplace transform and gives a table of Laplace transforms that are often used. For further details about Laplace transform, see Schiff [SCHI 1999] or Bellman and Roth [BELL 1994].

Suppose that is a piecewise-continuous function, defined at least for , and is of exponential order , meaning that it does not grow any faster than the exponential :

for some constant M. Then the Laplace transform of , denoted by , is defined by the integral

D.1

for any complex number s such that its real part Re.

Important pairs are given in Table D.1.

Table D.1 ...