4.1.6. Properties of the unilateral Laplace transform

These are from the Wikipedia page on the Laplace transform

Laplace Transform Properties

	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	\(x(t)\ast y(t)\)	\(X(s) Y(s)\)