5.1.4 Given an oriented piecewise-smooth surface that is bounded by a simple, closed, piecewise-smooth boundary curve with positive orientation, and a vector field whose components have continuous partial derivatives on an open region in three-dimensional Euclidean space. Then the line integral of this vector field along the boundary curve equals the flux of the curl of the vector field across the surface.
5.1.4 Given an oriented piecewise-smooth surface that is bounded by a simple, closed, piecewise-smooth boundary curve with positive orientation, and a vector field whose components have continuous partial derivatives on an open region in three-dimensional Euclidean space. Then the line integral of this vector field along the boundary curve equals the flux of the curl of the vector field across the surface.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TRUE OR FALSE?
![5.1.4 Given an oriented piecewise-smooth
surface that is bounded by a simple,
closed, piecewise-smooth boundary
curve with positive orientation, and a
vector field whose components have
continuous partial derivatives on an open
region in three-dimensional Euclidean
space. Then the line integral of this vector
field along the boundary curve equals the
flux of the curl of the vector field across
the surface.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cc3d051-9d70-4244-aafe-3a1afd16e3d9%2F3f1fd870-013f-4956-bd12-45c0321ca1d6%2Fmvfjq8h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.1.4 Given an oriented piecewise-smooth
surface that is bounded by a simple,
closed, piecewise-smooth boundary
curve with positive orientation, and a
vector field whose components have
continuous partial derivatives on an open
region in three-dimensional Euclidean
space. Then the line integral of this vector
field along the boundary curve equals the
flux of the curl of the vector field across
the surface.
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