Category:Dirac Delta Function
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This category contains results about the Dirac delta function.
Definitions specific to this category can be found in Definitions/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:
- $\map \delta x = \ds \lim_{\epsilon \mathop \to 0} \map {F_\epsilon} x$
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Dirac Delta Function"
The following 16 pages are in this category, out of 16 total.
I
- Integral of Dirac Delta Function by Continuous Function over Reals
- Integral of Dirac Delta Function over Reals
- Integral of Shifted Dirac Delta Function by Continuous Function over Reals
- Integral to Infinity of Dirac Delta Function
- Integral to Infinity of Dirac Delta Function by Continuous Function
- Integral to Infinity of Shifted Dirac Delta Function by Continuous Function