# Questions tagged [dirac-delta]

This tag is for questions involving the Dirac delta function, either in the informal sense, or in the distribution sense. The Dirac delta function is a mathematical construct which is called a generalized function or a distribution and was originally introduced by the British theoretical physicist Paul Dirac.

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### Question about identity of Dirac delta function [duplicate]

I am trying to understand an identity of the $\delta$-function written on this Wikipedia page: \int \mathrm{d} x \; f(x) \delta[g(x)] = \sum\limits_i \frac{f(x_i)}{\left| \frac{dg(x_i)...
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### Showing $u =0$ for a particular laplace equation.

Given open $\Omega\subset \mathbb{R}^n$ with smooth enough boundary, if for $x_0 \in \Omega$ there exists $u \in C^2(\Omega\setminus\{x_0\})$( we may as well take $u$ as smooth as we want) that ...
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### How to write $\delta (f(x))$ in terms of $\delta (x)$?

I've seen this identity in my electrodynamics book: $$\delta (f(x))=\sum_i{ \frac{1}{|{df\over dx}(x_i)|}\delta (x-x_i)}$$ Where $x_i$ shows the $i$th zero of $f(x)$. How can I prove it? I've tried ...
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### Dirac delta function divided by Dirac delta function

Is the following defined: (Dirac delta function divided by Dirac delta function) $$f = \frac{\delta}{\delta} = ?$$
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### Heaviside unit step- and delta function

The following question is right from the book: Show that $$H(x-x_i) = \int_{-\infty}^x \delta(x_0-x_i)dx_0\,$$ satisfies  H(x-x_i) \equiv \begin{cases} 0 & x < x_i \\ 1 &...
$2y''+y'+2y=\delta(t-5)$ $y(0)=0, y'(0)=0$ Consider the system given by ODE above in which an oscillation is excited by a unit impulse at $t=5$. Suppose that it is desired to bring the system to ...