Documentation

ilaplace

Inverse Laplace transform

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

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)

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

Related Examples

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