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This dynamic Java applet developed with support from the NSF (Dynamic Visualization Tools for Multivariable Calculus, DUE-CCLI Grant #0736968)) allows the user to simultaneously graph multiple 3D surfaces, space curves, parametric surfaces, vector fields, contour plots, and more in a freely rotatable 3D plot. This tool is intended as a dynamic visualization and exploration environment for multivariable calculus. Use it to illustrate the geometric relationships of many of the concepts of multivariable calculus, including dot and cross products, velocity and acceleration vectors for motion in the plane and in space, the TNB-frame, the osculating circle and curvature, surfaces, contour plots and level surfaces, partial derivatives, gradient vectors and gradient fields, Lagrange multiplier optimization, double integrals as volume, defining the limits of integration for double and triple integrals, parametric surfaces, vector fields, line integrals, and more. See the corresponding web page for documentation and a list of guided explorations developed for students to use with this exploration applet.

This set of four pages leads students through an introduction to standard set theory notation and the use of Venn diagrams. Java applets are used to give students random questions to which they respond with a graphical (point and click) interface.

Graph functions, zoom on points, and find points of intersection of multiple graphs.