8.7 Laplace Transforms
Axiom can compute some forward Laplace transforms, mostly
Laplace transform of elementary function:elementary
functions transform:Laplace not involving logarithms, although
some cases of special functions are handled.
To compute the forward Laplace transform of with respect to
and express the result as , issue the command
.
laplace(sin(a*t)*cosh(a*t)-cos(a*t)*sinh(a*t), t, s)
Type: Expression Integer
Here are some other non-trivial examples.
laplace((exp(a*t) - exp(b*t))/t, t, s)
Type: Expression Integer
laplace(2/t * (1 - cos(a*t)), t, s)
Type: Expression Integer
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
Type: Expression Integer
laplace((cos(a*t) - cos(b*t))/t, t, s)
Type: Expression Integer
Axiom also knows about a few special functions.
laplace(exp(a*t+b)*Ei(c*t), t, s)
Type: Expression Integer
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
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Type: Expression Integer
When Axiom does not know about a particular transform,
it keeps it as a formal transform in the answer.
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
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Type: Expression Integer