InverseLaplaceTransform

InverseLaplaceTransform[expr,s,t]

gives the inverse Laplace transform of expr.

InverseLaplaceTransform[expr,{s1,s2,…},{t1,t2,…}]

gives the multidimensional inverse Laplace transform of expr.

Details

  • The inverse Laplace transform of a function is defined to be , where γ is an arbitrary positive constant chosen so that the contour of integration lies to the right of all singularities in .
  • In TraditionalForm, InverseLaplaceTransform is output using ℒ-1. »

Examples

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Basic Examples  (2)

Scope  (4)

Rational functions:

Elementary functions:

Special functions:

TraditionalForm formatting:

Generalizations & Extensions  (1)

Multidimensional inverse Laplace transform:

Applications  (2)

Compute the step response to the linear system with transfer function :

Solve a differential equation using Laplace transforms:

Solve for the Laplace transform:

Find the inverse transform:

Apply initial conditions:

Find the solution directly using DSolve:

Properties & Relations  (2)

Use Asymptotic to compute an asymptotic approximation:

InverseLaplaceTransform and LaplaceTransform are mutual inverses:

Possible Issues  (1)

InverseLaplaceTransform assumes that the result is defined for non-negative t:

The result remains valid after multiplication with HeavisideTheta:

Neat Examples  (1)

InverseLaplaceTransform of a MeijerG function:

Introduced in 1999
 (4.0)