Definition:Dirac Delta Function/Definition 1

Definition
Let $\epsilon \in \R_{>0}$ be a (strictly) positive real number.

Consider the real function $F_\epsilon: \R \to \R$ defined as:


 * $\map {F_\epsilon} x := \begin{cases}

0 & : x < 0 \\ \dfrac 1 \epsilon & : 0 \le x \le \epsilon \\ 0 & : x > \epsilon \end{cases}$

The Dirac delta function is defined as:


 * $\map \delta x := \ds \lim_{\epsilon \mathop \to 0} \map {F_\epsilon} x$

Also see

 * Equivalence of Definitions of Dirac Delta Function