ilaplace (Symbolic Math Toolbox)

ilaplace
Inverse Laplace transform.

Syntax

F = ilaplace(L)
F = ilaplace(L,y)
F = ilaplace(L,y,x)

Description
F = ilaplace(L) is the inverse Laplace transform of the scalar symbolic object L with default independent variable s. The default return is a function of t. The inverse Laplace transform is applied to a function of s and returns a function of t.

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

By definition

where c is a real number selected so that all singularities of L(s) are to the left of the line s = c, i.

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

Here y is a scalar symbolic object.

F = ilaplace(L,y,x) takes F to be a function of x and L a function of y instead of the default variables t and s, respectively.

Examples

Inverse Laplace Transform
MATLAB Command

f = 1/s^2

ilaplace(f)
returns

t

g = 1/(t-a)^2

ilaplace(g)
returns

x*exp(a*x)

f = 1/(u^2-a^2)

ilaplace(f,x)
returns

1/2/a*exp(a*x)-1/2/a*exp(-a*x)

f = s^3*v/(s^2+v^2)

laplace(f,v,x)
returns

s^3*cos(s*x)

Inverse Laplace Transform	MATLAB Command
	`f = 1/s^2` `ilaplace(f)` returns `t`
	`g = 1/(t-a)^2` `ilaplace(g)` returns `xexp(ax)`
	`f = 1/(u^2-a^2)` `ilaplace(f,x)` returns `1/2/aexp(ax)-1/2/aexp(-ax)`
	`f = s^3v/(s^2+v^2)` `laplace(f,v,x)` returns `s^3cos(s*x)`

See Also
ifourier, iztrans, laplace

ifourier imag