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algebraic arc length aXb-c bound vector closed smooth curve collinear const continuous first partial coordinate systems coplanar deduce defined dF/dz dimensions domain containing domain in three dv dw dx dy dxdy dxdydz dydz example exists express f Pdx f Qdy ffd£dxdy finite number fpdx Gauss gradient gral Green's lemma Green's theorem h2 dv h3 dw Hence i j k Laplacian Let F(x line integral midpoint mutually perpendicular origin parallel parametric equations partial derivatives PiP2 points Pi position vector positive triple prove real number respectively right-handed system scalar function scalar triple product Similarly skew curve smooth surface spherical coordinates Stokes surface integral tangent plane tangent vector theorem tion unit outer normal unit vector vector function vector with components write Eq written