Matlab: Laplace Transform

The examples below demonstrate the Laplace transforms and inverse Laplace transforms using Matlab symbolic number or variable.

Laplace Transform

L{1} = 1/s

>> x = sym(1);
>> laplace(x)

ans =

1/s

L{t} = 1/s²

>> syms t
>> laplace(t)

ans =

1/s^2

Inverse Laplace Transform

L^-1{1/s} = 1

>> syms s
>> ilaplace(1/s)

ans =

1

L^-1{1/(s-a)} = e^at where a = 2

>> ilaplace(1/(s-2))

ans =

exp(2*t)

L^-1{a²/(s²+a²)} = sin(at) where a = 1

>> ilaplace(1/(s^2+1))

ans =

sin(t)

Reference

Zill, D., Wright, W. S., & Cullen, M. R. (2011). Advanced engineering mathematics. 4th Edition. Jones & Bartlett Learning. p 197-198.

laplace / ilaplace - MathWorks Documentation