Laplace Transforms

Description

Sage can compute Laplace transforms. The Laplace transform of $t^2e^t - \sin t$ is computed as follows:

Sage Cell

Code

s, t = var('s, t')
f = t^2*exp(t) - sin(t)
f.laplace(t,s)


Options

Option

We can also compute the inverse Laplace transform of

(1)
\begin{align} F(s) = -\frac{1}{s^2 + 1} + \frac{2}{(s - 1)^3}. \end{align}

Code

s = var("s")
t = var("t")
F = -1/(s^2 + 1) + 2/(s - 1)^3
F.inverse_laplace(s,t)


Tags

Primary Tags: Differential Equations: Laplace transforms

Secondary Tags: Laplace transforms: Basic transformations, Inverse transformations

Related Cells

• desolve_laplace. Solving ordinary differential equations using Laplace transforms.