Title: Using technology to illustrate level curves

Level curves have long been a standard topic in both traditional and reform presentations of multivariate calculus. In some reform texts, level curve representations of functions are receiving increased emphasis. Thanks to technology, we can lift our illustrations of level curves from the page and present them in 3-space, where their meaning and import is more obvious. The simple act of rotating a 3 dimensional Maple plot with contour lines can teach a student more about level curves than countless flat diagrams.

• Level curves revealed in the top view of 3 dimensional surfaces, using Quicktime animations of a paraboloid and a hyperbolic paraboloid. Viewing these requires use of the free Quicktime player.
• Viewing level curves in Maple.
• Animating the rotations of the surfaces.
• Converting Maple animations to Quicktime movies.
• Instructions in pdf on using Excel in Calculus III.
• A related Excel worksheet which includes the diffusion demonstration.