What is the Divergence Theorem? Explain how it generalizes Green’s Theorem to three dimensions.

facas9

facas9

Answered question

2021-02-09

What is the Divergence Theorem? Explain how it generalizes Green’s Theorem to three dimensions.

Answer & Explanation

Nichole Watt

Nichole Watt

Skilled2021-02-10Added 100 answers

Divergence Theorem:
- Consider F be a vector field whose components consists of continuous first partial derivatives and considers be a piecewise smooth oriented closed surface.
- The flux of F across S in the direction of the surface’s outward unit normal field n equals the triple integral of the divergence grad*F over the solid region D bounded by the surface:
SFndσ=DFdV
Step 2
- The divergence theorem simplifies the normal (flux) form of Green’s
theorem in a two-dimensional region in the plane and a three-dimensional region in space.
The total flux of the field across the boundary bounding the region is equal to the integral of grad*F over the interior of the region.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Multivariable calculus

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?