Interactive Concept-Visualization Tools
To help you better understand some of the concepts of multivariable calculus, I’ve created some interactive Concept-Visualization Tools (CVTs), which are computer graphics that you can manipulate. The CVTs were created using LiveGraphics3D. To manipulate the CVTs, you can
- click and drag to rotate in any direction,
- shift + click and drag up/down to zoom in/out,
- shift + click and drag left/right to rotate around an axis coming out of the screen, and
- press Home to reset to the original view.
Most of these CVTs have parameters that you can change. In general, you can click and drag points or balls around to change the parameters.
The CVTs are Java applets, so you must have Java installed and properly configured in your browser for the CVTs to display. If you have trouble getting the CVTs to display in your browser, you can visit the LiveGraphics3D troubleshooting page for information on how to get the Java applets to work.
On occasion, even when Java is configured correctly, the CVTs don’t load the first time and one instead sees an error message. You can reload the page to see if the CVT will properly load. Sometimes, one needs to do this multiple times.
