Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In Gauss Divergence Theorem , $$\int \int_{\partial V} \textbf{F}\cdot\textbf{n}\,dS =\int \int \int_V \nabla\cdot\textbf{F}\,dx\,dy\,dz,$$ is there any restriction on the vector field $\textbf{F}$ ? Does it need to be in dimension three only ? Can I let it be $\textbf{F}=xyz$ where $x,y,z\in\mathbb{R}$ ?

share|cite|improve this question
1  
The concepts in the Divergence Theorem and Stoke's Theorem generalize to higher dimensions. Such generalizations make use of differential forms. See en.wikipedia.org/wiki/Stokes%27_Theorem#General_formulation – Ron Gordon Dec 28 '12 at 18:12
up vote 1 down vote accepted

$F=xyz$ is not a vector field. You can take a look at the wikipedia definitions. Yes, $F$ has to be continuous and differentiable.

See here: http://en.wikipedia.org/wiki/Divergence_theorem

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.