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ilaplace

  

inverse Laplace integral transform

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ilaplace(M)

ilaplace(M,y)

ilaplace(M,y, x)

Parameters

M

-

array or expression

y

-

variable expr is transformed with respect to y 

x

-

variable in transformed expression

Description

• 

The ilaplace(M) calling sequence computes the element-wise inverse Laplace transform of M.  The result, R, is formed as R[i,j] = ilaplace(M[i,j], y, x).

• 

ilaplace(L) is the inverse Laplace transform of the scalar L with default independent variable s.  If L is not a function of s, then L is  assumed to be a function of the independent variable returned by findsym(L,1).The default return is a function of t.

• 

If L = L(t), then ilaplace returns a function of x.

• 

By definition,

Ft=cIc+ILsⅇstⅆs,

where c is a real number selected so that all singularities of L(s) are to the left of the line s = c and the integration above proceeds with respect to s.

• 

ilaplace(L,y) makes F a function of the variable y instead of the default t.

• 

ilaplace(L,y,x) takes L to be a function of x instead of the default t. The integration is then with respect to y.

Examples

withMTM:

ilaplace1s2+4

sin2t2

(1)

ilaplace1t2+4

sin2x2

(2)

ilaplace1s2+4,w

sin2w2

(3)

ilaplacezs2+4,z,q

Dirac1,qs2+4

(4)

MMatrix1s2+4,zs2+4:

ilaplaceM

sin2t2zsin2t2

(5)

See Also

inttrans[invlaplace]

MTM[findsym]

MTM[ifourier]

MTM[iztrans]

MTM[laplace]