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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 Math Flash Forum Sharing Area applet provides students with practice with polar coordinates and the radian measure of angles through a simple, interactive game.
This Java applet allows the user to experiment with Riemann sums. It can also be used to approximate definite integrals or find upper and lower bounds to the exact value of a definite integral, using Riemann sums.