SAGE :The Unit Step Function (Heaviside Function)

The unit step function is defined as $$u_c(t)=\left\{ \begin{array}{ll} 0 & t\lt c \\ 1 & t \ge c \\ \end{array} \right.$$

We can define the unit step function in SageMath using the unit_step function or the Heaviside function. Evaluating the next cell will not produce any output, just creates the function.


We can now plot something like $u_3(t)$


Or

$$f(t)=\left\{ \begin{array}{ll} 0 & t\lt 2 \\ sin(6(t-2))+2 & 2 \leq t \lt 4 \\ 0 & t\geq 4 \\ \end{array} \right.$$

Find $\mathcal{L}\{u_3(t)\}$


Find $\mathcal{L}\{u_2(t)\cdot t^2\}$