## A Short Course in Vector Analysis |

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algebraic arbitrary arc length axdy bound vector closed bounded region closed smooth curve collinear const continuous first partial continuously differentiable coordinate systems coplanar deduce defined dF/dz directional derivative domain containing domain in three dxdy dxdydz equation implies example exists f Pdx finite number Gauss gradient gral Green's lemma Hence i j k Laplacian Let F(x line integral midpoint mutually perpendicular normal vector origin P2Pi parallel parametric equations partial derivatives point Pi position vector positive triple prove Q dy Q dzdx real number right-handed system scalar function scalar triple product Similarly skew curve smooth surface Solution spherical coordinates Stokes surface integral tangent plane tangent vector three space tion unit normal unit outer normal unit vector vector with components vector-valued function write Eq written