Symbolic Math Toolbox™

laplace - Laplace transform

Syntax

laplace(F)
laplace(F,t)
laplace(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.

L = L(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) = t⁴	`f = t^4` `laplace(f)` returns `24/s^5`
	`g = 1/sqrt(s)` `laplace(g)` returns `(pi/t)^(1/2)`
f(t) = e^–at	`f = exp(-a*t)` `laplace(f,x)` returns `1/(x + a)`

Laplace Transform

MATLAB^® Command

f(t) = t⁴