Can anyone help me with an explanation of the following notation. I am a bit confused:
Lets say we have some type of integral and in the end we write different differential, such as:
$$d\vec r ,\quad d^3\vec r,\quad dxdydz,\quad dV.$$
How are these with each other related? Can we express the first one in components, or the second one.
Any explanation would help. I am asking because i am looking at this thread:
And i don't understand it. First of all PDF (like normal distribution for example) have no differential part like there is for the velocity in the above link. And then what is the difference between maxwell velocity distribution and maxwell speed distribution.
What i know ( please correct me if i am wrong):
$dP(x)=f(x)dx$ which physically means that we are searching the probability that $x$ is in the interval $x$ and $x + dx$.
Then for the velocity/speed (i don't know which of the 2 terms to use) distribution (in 3D), in analogy with the above equation we would have:
$dP(\vec v)=f(\vec v)dv_x dv_y dv_z /$. Is $dv_x dv_y dv_z = d\vec v$ or $d^3 \vec v$. I am confused by the notations etc.