Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Gauss's_theorem
gptkb:divergence_theorem |
| gptkbp:application |
electromagnetism
fluid dynamics heat transfer |
| gptkbp:appliesTo |
three-dimensional Euclidean space
|
| gptkbp:category |
integral theorems
|
| gptkbp:field |
vector calculus
|
| gptkbp:firstPublished |
1813
|
| gptkbp:form |
∬_S F · dS = ∭_V (∇ · F) dV
|
| gptkbp:generalizes |
gptkb:Green's_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gauss's divergence theorem
|
| gptkbp:namedAfter |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:relatedTo |
gptkb:Stokes'_theorem
divergence vector field flux surface integral volume integral |
| gptkbp:requires |
closed surface
differentiable vector field |
| gptkbp:sentence |
The flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field inside the surface.
|
| gptkbp:usedIn |
gptkb:mathematics
engineering physics |
| gptkbp:bfsParent |
gptkb:Gauss's_theorem_(divergence_theorem)
|
| gptkbp:bfsLayer |
7
|