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

(pi/t)^(1/2)

f = exp(-a*t)

laplace(f,x)
returns

1/(x + a)

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

See Also

fourier, ilaplace, ztrans

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