Mixing
Interpretation of divergence theorem in $mathbb R^3$ with an identity
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I'm trying to solve this exercise:
Let $S$ be an open set of $mathbb R^3$ , and $W$ be a regular domain such that $overline{W}$ is include in S. Let $Fin C^{1}(S,mathbb R^3$).
If a $in$ $overline{W}$, show that:
$operatorname{div}F(a)space = displaystylelim_{text{Area}(overline{W}) rightarrow 0}frac{oint_{partial overline{W}} Fcdot mathrm ds}{text{Area}(overline{W})}$.
Thank you for your answers !
I tried to write the divergence theorem. I think the argument is simple- but I can't find it.
real-analysis vector-analysis
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
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add a comment |
$begingroup$
I'm trying to solve this exercise:
Let $S$ be an open set of $mathbb R^3$ , and $W$ be a regular domain such that $overline{W}$ is include in S. Let $Fin C^{1}(S,mathbb R^3$).
If a $in$ $overline{W}$, show that:
$operatorname{div}F(a)space = displaystylelim_{text{Area}(overline{W}) rightarrow 0}frac{oint_{partial overline{W}} Fcdot mathrm ds}{text{Area}(overline{W})}$.
Thank you for your answers !
I tried to write the divergence theorem. I think the argument is simple- but I can't find it.
real-analysis vector-analysis
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
$endgroup$
$begingroup$
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
$endgroup$
– mrtaurho
Jan 6 at 15:12
add a comment |
$begingroup$
I'm trying to solve this exercise:
Let $S$ be an open set of $mathbb R^3$ , and $W$ be a regular domain such that $overline{W}$ is include in S. Let $Fin C^{1}(S,mathbb R^3$).
If a $in$ $overline{W}$, show that:
$operatorname{div}F(a)space = displaystylelim_{text{Area}(overline{W}) rightarrow 0}frac{oint_{partial overline{W}} Fcdot mathrm ds}{text{Area}(overline{W})}$.
Thank you for your answers !
I tried to write the divergence theorem. I think the argument is simple- but I can't find it.
real-analysis vector-analysis
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
$endgroup$
I'm trying to solve this exercise:
Let $S$ be an open set of $mathbb R^3$ , and $W$ be a regular domain such that $overline{W}$ is include in S. Let $Fin C^{1}(S,mathbb R^3$).
If a $in$ $overline{W}$, show that:
$operatorname{div}F(a)space = displaystylelim_{text{Area}(overline{W}) rightarrow 0}frac{oint_{partial overline{W}} Fcdot mathrm ds}{text{Area}(overline{W})}$.
Thank you for your answers !
I tried to write the divergence theorem. I think the argument is simple- but I can't find it.
real-analysis vector-analysis
real-analysis vector-analysis
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
edited Jan 6 at 15:26
Cauchy is my master
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
asked Jan 6 at 15:08
Cauchy is my masterCauchy is my master
293
293
$begingroup$
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
$endgroup$
– mrtaurho
Jan 6 at 15:12
add a comment |
$begingroup$
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
$endgroup$
– mrtaurho
Jan 6 at 15:12
$begingroup$
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
$endgroup$
– mrtaurho
Jan 6 at 15:12
$begingroup$
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
$endgroup$
– mrtaurho
Jan 6 at 15:12
add a comment |
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Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :)
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– mrtaurho
Jan 6 at 15:12