Question

Is $\nabla\cdot\hat{\frac{r}{r^3}}=-\frac{1}{r^4}+\frac{1}{r}4\pi\delta\vec{r}$ correct?

score 109 · Answer 1 · 2018-03-06 08:35:48

109

Views

Is $\nabla\cdot\hat{\frac{r}{r^3}}=-\frac{1}{r^4}+\frac{1}{r}4\pi\delta\vec{r}$ correct?

Published on 06 Mar 2018 - 8:35

score 2k · Answer 2 · 2018-03-08 16:30:49

2k

Views

The distinction between "ordinary" functions and generalized functions.

Published on 08 Mar 2018 - 16:30

score 79 · Answer 3 · 2018-03-08 18:45:23

79

Views

Prove that $\lim_{k \to \infty} \int_{-\infty}^{\infty} \frac{ke^{-k^2x^2}}{\pi}h(x) = h(0)$

Published on 08 Mar 2018 - 18:45

score 161 · Answer 4 · 2026-03-24 23:23:28

161

Views

Time dependent PDE in polar coordinate

Published on 24 Mar 2026 - 23:23

score 588 · Answer 5 · 2026-03-22 15:06:02

588

Views

Laplace Transform with the Dirac Delta Function

Published on 22 Mar 2026 - 15:06

score 2.2k · Answer 6 · 2026-03-24 23:44:36

2.2k

Views

Can't understand a property of delta function and convolution

Published on 24 Mar 2026 - 23:44

score 274 · Answer 7 · 2018-03-09 21:42:00

274

Views

Taking the derivative of the limit representation of the Heaviside function

Published on 09 Mar 2018 - 21:42

score 291 · Answer 8 · 2026-03-22 13:15:51

291

Views

Dirac Delta's Ill-defineness Property

Published on 22 Mar 2026 - 13:15

score 709 · Answer 9 · 2026-03-24 20:42:38

709

Views

Delta function of form: $\frac 1 {4π} \nabla ^2 \frac 1 {\lvert r - {r'} \rvert}$

Published on 24 Mar 2026 - 20:42

score 103 · Answer 10 · 2018-03-12 17:07:25

103

Views

What does it mean by one Dirac measure and two Dirac measure

Published on 12 Mar 2018 - 17:07

score 38 · Answer 11 · 2018-03-13 08:37:22

38

Views

Understanding empirical probability densities in terms of Dirac measure

Published on 13 Mar 2018 - 8:37

score 77 · Answer 12 · 2018-03-14 15:23:04

77

Views

$v(x)\cdot \nabla_y \delta(x-y)\rightarrow \nabla_y\cdot\ v(y)\delta(x-y)$ Justification

Published on 14 Mar 2018 - 15:23

score 102 · Answer 13 · 2018-03-16 18:03:41

102

Views

Can the integral $\int_0^{\infty} \sin\big( [x-y]p \big) dp$ be related to a Dirac Delta function?

Published on 16 Mar 2018 - 18:03

score 998 · Answer 14 · 2026-03-22 08:14:42

998

Views

Proving the Delta Function Composition Identity

Published on 22 Mar 2026 - 8:14

score 91 · Answer 15 · 2018-03-20 07:09:08

91

Views

Let $f(x)=\delta(x) $ if $ x\in (-\infty,0] $ and $f(x)=0$ if $x\in (0,\infty)$. Then $I=\int_{-\infty}^{\infty}f(x)dx=?$

Published on 20 Mar 2018 - 7:09

List Question

Is $\nabla\cdot\hat{\frac{r}{r^3}}=-\frac{1}{r^4}+\frac{1}{r}4\pi\delta\vec{r}$ correct?

The distinction between "ordinary" functions and generalized functions.

Prove that $\lim_{k \to \infty} \int_{-\infty}^{\infty} \frac{ke^{-k^2x^2}}{\pi}h(x) = h(0)$

Time dependent PDE in polar coordinate

Laplace Transform with the Dirac Delta Function

Can't understand a property of delta function and convolution

Taking the derivative of the limit representation of the Heaviside function

Dirac Delta's Ill-defineness Property

Delta function of form: $\frac 1 {4π} \nabla ^2 \frac 1 {\lvert r - {r'} \rvert}$

What does it mean by one Dirac measure and two Dirac measure

Understanding empirical probability densities in terms of Dirac measure

$v(x)\cdot \nabla_y \delta(x-y)\rightarrow \nabla_y\cdot\ v(y)\delta(x-y)$ Justification

Can the integral $\int_0^{\infty} \sin\big( [x-y]p \big) dp$ be related to a Dirac Delta function?

Proving the Delta Function Composition Identity

Let $f(x)=\delta(x) $ if $ x\in (-\infty,0] $ and $f(x)=0$ if $x\in (0,\infty)$. Then $I=\int_{-\infty}^{\infty}f(x)dx=?$

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