A hemisphere H and a portion P of a paraboloid are shown. Suppose F is a vector field on ℝ 3 whose components have continuous partial derivatives. Explain why ∬ H curl F ⋅ d S = ∬ P curl F ⋅ dS
A hemisphere H and a portion P of a paraboloid are shown. Suppose F is a vector field on ℝ 3 whose components have continuous partial derivatives. Explain why ∬ H curl F ⋅ d S = ∬ P curl F ⋅ dS
Solution Summary: The author explains Stokes' Theorem: If S and S_2 are oriented surfaces with the same orientated boundary curve C and both satisfy the hypotheses of Stoke
A hemisphere
H
and a portion
P
of a paraboloid are shown. Suppose
F
is a vector field on
ℝ
3
whose components have continuous partial derivatives. Explain why
∬
H
curl
F
⋅
d
S
=
∬
P
curl
F
⋅
dS
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY