This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# LaplaceTransform

 LaplaceTransformgives the Laplace transform of expr. LaplaceTransformgives the multidimensional Laplace transform of expr.
• The Laplace transform of a function is defined to be .
• The lower limit of the integral is effectively taken to be , so that the Laplace transform of the Dirac delta function is equal to 1. »
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 Scope   (5)
Elementary functions:
Special functions:
Piecewise functions:
In these distributions, the integration region is taken to start at :
Multidimensional Laplace transform:
Integrals:
 Options   (2)
Specify the range for a parameter using Assumptions:
Use GenerateConditions->True to get parameter conditions for when a result is valid:
 Applications   (1)
Solve a differential equation using Laplace transforms:
Solve for the Laplace transform:
Find the inverse transform:
Find the solution directly using DSolve:
LaplaceTransform and InverseLaplaceTransform are mutual inverses:
Use NIntegrate for numerical approximation:
NIntegrate computes the transform for numeric values of the Laplace parameter s:
Simplification can be required to get back the original form:
LaplaceTransform done in terms of MeijerG:
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