Question

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

score 112 · Answer 1 · 2026-04-16 08:43:57

112

Views

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

Published on 16 Apr 2026 - 8:43

score 2k · Answer 2 · 2026-04-11 15:51:07

2k

Views

The distinction between "ordinary" functions and generalized functions.

Published on 11 Apr 2026 - 15:51

score 82 · Answer 3 · 2026-04-15 15:11:08

82

Views

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

Published on 15 Apr 2026 - 15:11

score 169 · Answer 4 · 2026-04-29 12:24:29

169

Views

Time dependent PDE in polar coordinate

Published on 29 Apr 2026 - 12:24

score 591 · Answer 5 · 2026-04-13 08:26:30

591

Views

Laplace Transform with the Dirac Delta Function

Published on 13 Apr 2026 - 8:26

score 2.2k · Answer 6 · 2026-05-10 13:48:21

2.2k

Views

Can't understand a property of delta function and convolution

Published on 10 May 2026 - 13:48

score 278 · Answer 7 · 2026-04-16 23:02:27

278

Views

Taking the derivative of the limit representation of the Heaviside function

Published on 16 Apr 2026 - 23:02

score 293 · Answer 8 · 2026-04-14 20:37:46

293

Views

Dirac Delta's Ill-defineness Property

Published on 14 Apr 2026 - 20:37

score 715 · Answer 9 · 2026-05-10 12:34:37

715

Views

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

Published on 10 May 2026 - 12:34

score 106 · Answer 10 · 2026-04-13 23:29:07

106

Views

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

Published on 13 Apr 2026 - 23:29

score 41 · Answer 11 · 2026-04-10 01:24:33

41

Views

Understanding empirical probability densities in terms of Dirac measure

Published on 10 Apr 2026 - 1:24

score 80 · Answer 12 · 2026-04-14 00:35:57

80

Views

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

Published on 14 Apr 2026 - 0:35

score 105 · Answer 13 · 2026-04-14 21:37:49

105

Views

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

Published on 14 Apr 2026 - 21:37

score 1k · Answer 14 · 2026-04-08 16:26:07

1k

Views

Proving the Delta Function Composition Identity

Published on 08 Apr 2026 - 16:26

score 94 · Answer 15 · 2026-04-16 09:21:41

94

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 16 Apr 2026 - 9:21

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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