Laplace and inverse laplace transformation of unit step functions u(t).

[thepatient]

Homework Statement

So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this.

The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0.

The laplace transformation chart that I have has two columns, the column on the left shows f(t) and the column on the right shows inverse laplace{f(t)} = F(s) for the corresponding f(t) on the left. Under f(t), both u(t) and 1 are on the same row as F(s) = 1/s. Does this mean that if I take the inverse laplace of 1/s, I can choose between using 1 or u(t)?

Thanks.

 

[fzero]

The Laplace transform involves the domain $t\in [0,\infty)$. Both $f(t)=1$ and $u(t)$ are the same on this domain, so there's no ambiguity in computing the inverse Laplace transform.

 

[thepatient]

The Laplace transform involves the domain $t\in [0,\infty)$. Both $f(t)=1$ and $u(t)$ are the same on this domain, so there's no ambiguity in computing the inverse Laplace transform.

Thanks.

Thats what I thought.