Applet: A change of variables for an electrode tip domain changes volume
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Applet loading
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.
Applet links
This applet is found in the pages
- Triple integral change of variables story
- Volume calculation for changing variables in triple integrals
Notation systems
More information on notation systems
General information about three.js applets
The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.