Here is a short list of some of the main topics covered so far:

• Power series (good approximation at a point)
• Curvilinear coordinates ($d\rr$; line, surface, and volume integrals)
• Finding the electrostatic potential $V(\rr)$ (from either $\rho$ or $\EE$)
• Finding the electric field $\EE(\rr)$ (from either $\rho$ or $V$)

Figure 1: The relationships between $V$, $\EE$, and $\rho$.

It is possible to determine any of $\rho$, $V$, and $\EE$ from any one of the others; see Figure 1. Notice that moving up the diagram corresponds to integration and moving down the diagram corresponds to differentiation. We've only covered 4 of these 6 relationships so far, namely \begin{eqnarray*} \hbox{$1$: }& V(\rr) &= \int {1\over 4\pi\epsilon_0} {\rho(\rrp)\,d\tau'\over|\rr-\rrp|} \\ \hbox{$2$: }& \EE(\rr) &= \int {1\over 4\pi\epsilon_0} {\rr-\rrp\over|\rr-\rrp|^3} \>\rho(\rrp)\,d\tau'\\ \hbox{$3$: }& V(\rr) &= -\int_{\rr_0}^{\rr} \EE(\rr') \cdot d\rr' \\ \hbox{$5$: }& \EE(\rr) &= -\grad V(\rr) \end{eqnarray*} The remaining 2 relationships will be covered in the next class, showing how to obtain $\rho$ from $V$ or $\EE$,