Dirac Delta Function

The dirac delta function is defined as follows:

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

Properties

The Dirac Delta Function satisfies the following properties:

1. $\delta (t-c)=0\,\!$ for all $t\neq c$
2. $\int _{c-\epsilon }^{c+\epsilon }\delta (t-c)\,\mathrm {d} t=1$ for any $\epsilon >0$
3. $\int _{c-\epsilon }^{c+\epsilon }f(t)\,\delta (t-c)\,\mathrm {d} t=f(t)$ for any $\epsilon >0$