The Laplace transform pairs a function of a real coordinate, call it
, with
, with a different function of a complex
coordinate
:
Use tables to find the equations satisfied by from these
satisfied by
. Solve for
and look up the corresponding
in the tables.
Table 7.1 lists important properties of the Laplace
transform and table 7.2 gives example Laplace transform
pairs. In the tables, ,
,
, and
are constants, normally
positive,
is a natural number, and
In many cases, is physically time, since time is most likely
to satisfy the constraints
and coefficients independent
of
. Also, the Laplace transform likes initial conditions at
, not boundary conditions at both
and
.