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laplace

  

Laplace integral transform

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

laplace(M)

laplace(M,s)

laplace(M,t, s)

Parameters

M

-

array or expression

t

-

variable

s

-

variable

Description

• 

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

• 

If F = F(s), then laplace returns a function of t.

• 

By definition,

Ls=0Ftⅇtsⅆt

where the integration above proceeds with respect to t.

• 

laplace(F,x) makes L a function of the variable x instead of the default s.

• 

laplace(F,z,x) makes L a function of x instead of the default s. The integration is then with respect to z.

• 

The laplace(M) function computes the element-wise Laplace transform of M.  The result, R, is formed as R[i,j] = laplace(M[i,j]).

Examples

withMTM:

laplaceBesselI0,2t

1s24

(1)

laplaceBesselI0,2s

1t24

(2)

laplaceBesselI0,2t,x

1x24

(3)

laplaceBesselI0,z2t,z,x

14t2+x2

(4)

MMatrixBesselI0,2t,BesselI0,z2t:

laplaceM

1s241s24z2

(5)

See Also

inttrans[laplace]

MTM[findsym]

MTM[fourier]

MTM[ilaplace]

MTM[ztrans]