+and
+\begin{eqnarray}
+dr&=&\frac{\partial r}{\partial x}dx +
+ \frac{\partial r}{\partial y}dy +
+ \frac{\partial r}{\partial z}dz\\
+d\theta&=&\frac{\partial \theta}{\partial x}dx +
+ \frac{\partial \theta}{\partial y}dy +
+ \frac{\partial \theta}{\partial z}dz\\
+d\phi&=&\frac{\partial \phi}{\partial x}dx +
+ \frac{\partial \phi}{\partial y}dy +
+ \frac{\partial \phi}{\partial z}dz\\
+\end{eqnarray}
+and vectorial translations using the Jacobi matrix are given by matrix multiplications
+\begin{equation}
+d\vec{r}(x,y,z)=Jd\vec{\tilde{r}}(r,\theta,\phi)
+\end{equation}
+and
+\begin{equation}
+d\vec{\tilde{r}}(r,\theta,\phi)=J^{-1}d\vec{r}(x,y,z) \text{ .}
+\end{equation}
+$J$ and $J^{-1}$ are explicitily given by