Dirac Delta Function

The dirac delta function is defined as follows:

$\delta (t)=\{\begin{array}{ll}\mathrm{\infty }& t=0\\ 0& \text{otherwise}\end{array}$

Properties

The Dirac Delta Function satisfies the following properties:

1. $\delta (t-c)=0$ for all $t\ne c$
2. $\underset{c-ϵ}{\overset{c+ϵ}{\int }}\delta (t-c)\mathrm{d}t=1$ for any $ϵ>0$
3. $\underset{c-ϵ}{\overset{c+ϵ}{\int }}f(t)\delta (t-c)\mathrm{d}t=f(t)$ for any $ϵ>0$