Green's, Stoke's and Divergence Theorem Concepts
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Divergence Theorem?
Back
The Divergence Theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the region enclosed by the surface.
2.
FLASHCARD QUESTION
Front
What does Stokes' Theorem state?
Back
Stokes' Theorem relates a surface integral of a vector field over a surface to a line integral of the vector field over the boundary curve of the surface.
3.
FLASHCARD QUESTION
Front
What is Green's Theorem?
Back
Green's Theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by the curve.
4.
FLASHCARD QUESTION
Front
What is the primary application of the Divergence Theorem?
Back
To convert surface integrals into volume integrals, allowing for easier computation of flux.
5.
FLASHCARD QUESTION
Front
How does Stokes' Theorem apply to vector fields?
Back
It allows the evaluation of a line integral of a vector field around a closed curve by relating it to a surface integral over the surface bounded by the curve.
6.
FLASHCARD QUESTION
Front
What is the relationship between Green's Theorem and Stokes' Theorem?
Back
Green's Theorem is a special case of Stokes' Theorem in two dimensions.
7.
FLASHCARD QUESTION
Front
What is the formula for the Divergence Theorem?
Back
∮_S **F** • d**S** = ∫∫∫_V div(**F**) dV, where S is the closed surface and V is the volume.
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