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 bapp04-math-0001 is a piecewise-continuous function, defined at least for bapp04-math-0002, and is of exponential order bapp04-math-0003, meaning that it does not grow any faster than the exponential bapp04-math-0004:


for some constant M. Then the Laplace transform of bapp04-math-0007, denoted by bapp04-math-0008, is defined by the integral

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

Important pairs are given in Table D.1.

Table D.1 ...

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