Category:Definitions/Dirac Delta Function

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This category contains definitions related to Dirac Delta Function.
Related results can be found in Category:Dirac Delta Function.


Definition 1

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:

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


Definition 2

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

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

$\map {F_\epsilon} x := \begin {cases} 0 & : x < -\epsilon \\ \dfrac 1 {2 \epsilon } & : -\epsilon \le x \le \epsilon \\ 0 & : x > \epsilon \end {cases}$


The Dirac delta function is defined as:

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