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ilaplace

Inverse Laplace transform

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Syntax

ilaplace(F, s, t)

Description

ilaplace(F, s, t) computes the inverse Laplace transform of the expression F = F(s) with respect to the variable s at the point t.

The inverse Laplace transform can be defined by a contour integral in the complex plane:

,

where c is a suitable complex number.

If ilaplace cannot find an explicit representation of the transform, it returns an unevaluated function call. See Example 3.

If F is a matrix, ilaplace applies the inverse Laplace transform to all components of the matrix.

To compute the direct Laplace transform, use laplace.

Examples

Example 1

Compute the inverse Laplace transforms of these expressions with respect to the variable s:

ilaplace(1/(a + s), s, t)

ilaplace(1/(s^3 + s^5), s, t)

ilaplace(exp(-2*s)/(s^2 + 1) + s/(s^3 + 1), s, t)

Example 2

Compute the inverse Laplace transform of this expression with respect to the variable s:

f := ilaplace(1/(1 + s)^2, s, t)

Evaluate the inverse Laplace transform of the expression at the points t = - 2 t0 and t = 1. You can evaluate the resulting expression f using | (or its functional form evalAt):

f | t = -2*t_0

Also, you can evaluate the inverse Laplace transform at a particular point directly:

ilaplace(1/(1 + s)^2, s, 1)

Example 3

If laplace cannot find an explicit representation of the transform, it returns an unevaluated call:

ilaplace(1/(1 + sqrt(t)), t, s)

laplace returns the original expression:

laplace(%, s, t)

Example 4

Compute this inverse Laplace transform. The result is the Dirac function:

ilaplace(1, s, t)

Related Examples

Parameters

F

Arithmetical expression or matrix of such expressions

s

Identifier or indexed identifier representing the transformation variable

t

Arithmetical expression representing the evaluation point

Return Values

Arithmetical expression or unevaluated function call of type ilaplace. If the first argument is a matrix, then the result is returned as a matrix.

Overloaded By

F

See Also

MuPAD Functions

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