# Math Insight

### Applet: A change of variables for an electrode tip domain changes volume

A change of variables $\cvarf$ maps a rectangular solid $\dlv^*$ (first panel, in red) onto the the electrode tip $\dlv$ (second panel, in blue). It maps each small region of $\dlv^*$ onto a region of a different size in $\dlv$. You can move the highlighted red region in $\dlv^*$ and the highlighted blue region in $\dlv$ by dragging them with your mouse. As you move one region, the corresponding region in the other domain is highlighted. Notice that the red region has a different volume than the corresponding blue region. Especially when the blue region is near the electrode tip, the highlighted blue region is much smaller than the red region.