This applet is designed to build intuition about line integrals.

- The applet has a control window and 4 graphics windows.
- The first graphical window is the domain window. It contains a movable hot spot that focuses on a point in the graph.
- There are windows for an x-slice and a y-slice, the two cross sections of the 3-D graph obtained by holding y and x, respectively, constant at the hot spot. On the control panel there are check boxes to add the appropriate tangent line to each of these graphs.
- The fourth window gives a graph of the surface. If the tangent lines are made visible on the slices, they will also be visible here. An additional checkbox makes the tangent plane visible. It should be noted that the tangent plane, if it exists, is the plane that contains the two tangent lines for the slice curves.

Things to notice:

- For the default vector field, F = (x-y, x+y) the integral remains conststant if the curve is simply translated.
- For vector fields like F = (x, y), that are the gradient of a function, the integral is zero for any simply closed path of integration.

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University. It is used with permission. Go to the Banchoff Applet Help page.

Return to the Banchoff Applet page.

Return to the SLU Calculus Applet page.

Return to the Saint Louis University Department of Mathematics and Computer Science home page

Last updated By Mike May, S.J. , October 6, 2006.