Properties of the unilateral Laplace transform
==============================================

These are from the `Wikipedia page on the Laplace
transform <https://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems>`_


.. list-table:: **Laplace Transform Properties**
   :header-rows: 1
   :class: tablefullwidth

   * - 
     - Time Domain
     - $s$-Domain
     - Remark
       
   * - Linearity
     - $a\,x(t)+b\,y(t)$
     - $a\,X(s)+b\,Y(s)$
     - 

   * - Differentiation
     - $x'(t)$
     - $sX(s)$
     - $x(0)=0$       

   * - Integration
     - $\int_0^t f(u)du$
     - $\frac{1}{s}X(s)$
     -

   * - Convolution
     - $x(t)\ast y(t)$
     - $X(s) Y(s)$
     -