E has counter clockwise orientation then p x y dx qx

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Unformatted text preview: rientation (i.e. has counter-clockwise orientation), then P (x, y ) dx + Q(x, y ) dy = ∂D D ∂ Q ∂P − ∂x ∂y dA . Stokes’s Theorem: (∇ × F ) • n dA = S F • dr . ∂S (If n is pointing right at you then orient ∂S in a positive fashion (i.e. counterclockwise fashion, typically) to make the identity hold.) Spherical Coordinates: x = ρ sin φ cos θ y = ρ sin φ sin θ 1 z = ρ cos φ dV = ρ2 sin φ dρ dφ dθ . Second Derivative Test: Suppose the second partial derivatives of f are co...
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This document was uploaded on 02/15/2014 for the course MATH 222 at Kansas State University.

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