The Divergence (Gauss) Theorem

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This educational Demonstration, primarily for vector calculus students, presents a surface whose parametric equations are very similar to those of the unit sphere (but differ by a factor of in ). The divergence (Gauss) theorem holds for the initial settings, but fails when you increase the range value because the surface is no longer closed on the bottom. It becomes closed again for the terminal range value, but the divergence theorem fails again because the surface is no longer simple, which you can easily check by applying a cut.

Contributed by: Nick Bykov (March 2011)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.