Laplace Transform Determination/Differentiation with Respect to Parameter

Solution Technique for Laplace Transform

To find the Laplace transform of a function $f$, one can evaluate it as follows:

Let $\map f t$ be expressible in the form:

$\map f t = \dfrac \d {\d a} \map g {a, t}$

Then it may be possible to express:

$\map {\dfrac \d {\d a} } {\laptrans {\map g {a, t} } } = \laptrans {\map {\dfrac \d {\d a} } {\map g {a, t} } }$

Examples

Laplace Transform Determination/Differentiation with Respect to Parameter/Examples

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Methods of Finding Laplace Transforms: $4$. Differentiation with respect to a parameter