Suppose S and C satisfy the hypotheses of Stokes’ Theorem and f, g have continuous second-order partial derivatives. Use Exercise 24 and 26 in Section 16.5 to show the following. (a) ∫ C ( f ∇ g ) ⋅ d r = ∬ S ( Δ f × ∇ g ) ⋅ d S (b) ∫ C ( f ∇ f ) ⋅ d r = 0 (c) ∫ C ( f ∇ g + g ∇ f ) ⋅ d r = 0
Suppose S and C satisfy the hypotheses of Stokes’ Theorem and f, g have continuous second-order partial derivatives. Use Exercise 24 and 26 in Section 16.5 to show the following. (a) ∫ C ( f ∇ g ) ⋅ d r = ∬ S ( Δ f × ∇ g ) ⋅ d S (b) ∫ C ( f ∇ f ) ⋅ d r = 0 (c) ∫ C ( f ∇ g + g ∇ f ) ⋅ d r = 0
Solution Summary: The author explains the Stokes' Theorem: Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed, piece
Suppose S and C satisfy the hypotheses of Stokes’ Theorem and f, g have continuous second-order partial derivatives. Use Exercise 24 and 26 in Section 16.5 to show the following.
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