laplace (Symbolic Math Toolbox)

Laplace transform.

Syntax

laplace(F)
laplace(F,t)
fourier(F,w,z)

Description

L = laplace(F) is the Laplace transform of the scalar symbol F with default independent variable t. The default return is a function of s. The Laplace transform is applied to a function of t and returns a function of s.

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

By definition

where t is the symbolic variable in F as determined by findsym.

L = laplace(F,t) makes L a function of t instead of the default s.

Here L is returned as a scalar symbol.

L = laplace(F,w,z) makes L a function of z and F a function of w instead of the default variables s and t, respectively.

Examples

Laplace Transform
MATLAB Command

f = t^4

laplace(f)
returns

24/s^5

g = 1/sqrt(s)

laplace(g)
returns

1/s^(1/2)*pi^(1/2)

f = exp(-a*t)

laplace(f,x)
returns

1/(x + a)

f = 1 - cos(t*v)

laplace(f,v,x)
returns

1/x-x/(x^2+t^2)

Laplace Transform	MATLAB Command
	`f = t^4` `laplace(f)` returns `24/s^5`
	`g = 1/sqrt(s)` `laplace(g)` returns `1/s^(1/2)*pi^(1/2)`
	`f = exp(-a*t)` `laplace(f,x)` returns `1/(x + a)`
	`f = 1 - cos(t*v)` `laplace(f,v,x)` returns `1/x-x/(x^2+t^2)`