PX275 - B1e - spherical polar coordinates

\begin{matrix} x & = ρ \cos ϕ & = r \sin θ \cos ϕ \\ y & = ρ \sin ϕ & = r \sin θ \sin ϕ \\ z & = r \cos θ \end{matrix}

\begin{matrix} θ \in [0, π] \\ ϕ \in [0, 2 π] \\ ρ \in [0, \infty) \end{matrix}

surface and volume elements

d S = d ϕ \cdot r d θ = r^{2} \sin θ d ϕ d θ

\1\n\2\n