d(V) = d(4*pi*rho^3/3)*d(theta/2/pi)*d((1 - cos(phi))/2) = 4*pi*rho^2*d(rho)*d(theta)/2/pi*sin(phi)*d(phi)/2 = rho^2*sin(phi)*d(rho)*d(theta)*d(phi)
In spherical coordinates, d(V) is equal to the product of the following three factors.d(4*pi*rho^3/3) = 4*pi*rho^2*d(rho)d(theta/2/pi) = d(theta)/2/pid((1 - cos(phi))/2) = sin(phi)*d(phi)/2
4*pi*rho^3/3 = volume(sphere)0 <= theta/2/pi <= 1since0 <= theta <= 2*pi0 <= (1 - cos(phi))/2 <= 1since0 <= phi <= pi
The variables are correctly labeled, or defined, in the accompanying image.
>>16536681who gives a shit?
>>16538951>who gives a shit?This board is /sci/, remember?And this thread isn't your toilet!
>>16536371This is illegible without MathJaX
>>16537731i've seen every permutation of "correct" labels.i stopped remembering what the mathematicians, physicists, and engineers all say is "correct", and just reason out what convention the problem at hand decides to use
>>16539857The conventional physics method is retardedThe mathchad way has theta being consistent with polar/cylindrical
>>16539846>>16539857>>16540129the elephant in the room (or thread):>>16538951>who gives a shit?
