I'm not sure if I understand what you mean. Actually, I really don't like the square and arctan expressions either, but how else would you do it? You mean expressing ##x_1## and ##x_2## in terms of ##r## and ##\theta## like ## x_1 = r cos \theta ## and ## x_2 = r sin \theta ##? But if I then...
Okay, thanks for the tipps about the notation and sorry again for the confusion about the vector identity! :-) I tried to come forward now by considering
## r = \sqrt{x_1^2 + x_2^2} ##
## \theta = arctan(\frac{x_2}{x_1}) ##
## \frac{dr}{dx_1} = \frac{ x_1}{\sqrt{x_1^2 + x_2^2}} = \frac{...
But ## x \in R^2 ## is a vector ## x = (x_1,x_2)^T ## and how is ## \frac{1}{vector} ## is defined?
Okay, i started once again:
##x \in R^2## is a vector with the components ##x = (x_1,x_2)^T##
$$
\frac{ \partial (x_1/|x|^2) }{\partial x_1} + \frac{ \partial (x_2/|x|^2)}{ \partial x_2} =\\
-...
Actually by saying that ## x \in R^2 ## i always mean ## \int dx := \int d(x_1,x_2) ##, i definately should have stated that explicitely. Okay, i going to start from scratch with the distributional derivative for my vector field :-)
$$ <\frac{d}{dx_1} \frac{x}{|x|^2} + \frac{d}{dx_2}...
Homework Statement
Show that $$div ( \frac{x}{|x|^2} ) = 2 \pi \delta_{(0,0)}$$ with ## x \in R^2 \ \{ 0 \} ## and ## \delta_{(0,0)} ## beeing the dirac delta distribution with pole in ## (0,0) ##.
Homework Equations
## div (f(x)) = \nabla \cdot (f(x)) = f_{x_1} + f_{x_2} ##
The distribution...
Hey, I'm watching it too. I also think it's really great produced. Which special part from last nights episode are you talking about?
I haven't even watched X-Men, so i had to google the background story to find out about the original "Legion" Character in the X-Men universe...
Hi! I recently learned about the Alpha decay, where the atomic Nukleus emittes Alpha-Particles. I was wonderin if a material, which emittes such Alpha Particles has a surplus of electrons and so a negativ electronic charge after the decay. Because it loses Protons but stays with the...
Hi!
We were recently discussing if time appears quantified. I found the theory about "chronons" (quantums of time) on Wikipedia and I know, those are very theoretical constructs and as far as I found out there is no current research if chronons even exist. But I was wondering if somebody has an...
Hello,
I study technical physics at the technical university in Vienna. I'll start my third semester in october and I'm looking forward to interesting discussions in this online forum! :-)
cu,
kariosx