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 symvar.

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

Laplace Transform

MATLAB Command

f(t) = t⁴