to be careful to choose a parametrization r(u, v) that determines the correct counterclock- wise orientation on the surface S. Otherwise, the equation JJ CT curl(F). ndo = F. dr as will not be true because the incorrect orientation will cause the surface integral (on the left) to be the negative of its correct value.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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True or false and why

to be careful to choose a parametrization r(u, v) that determines the correct counterclock-
wise orientation on the surface S. Otherwise, the equation
JJ CT
curl(F). ndo =
F. dr
as
will not be true because the incorrect orientation will cause the surface integral (on the
left) to be the negative of its correct value.
Transcribed Image Text:to be careful to choose a parametrization r(u, v) that determines the correct counterclock- wise orientation on the surface S. Otherwise, the equation JJ CT curl(F). ndo = F. dr as will not be true because the incorrect orientation will cause the surface integral (on the left) to be the negative of its correct value.
When applying Stokes' theorem to a vector field F on a surface S in R³ we have
Transcribed Image Text:When applying Stokes' theorem to a vector field F on a surface S in R³ we have
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