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Vector Functions of a Single Variable
Scalar and Vector Fields
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A X B angle arc length axes axis B X C charge component of F compute conservative constant coordinate curves coordinate system curl F curvilinear coordinates cylindrical coordinates defined denote density differentiable directed line segment div F divergence theorem domain dt dt equals equations example exercise expression field F figure Find flow lines flux force formula function geometrical given grad gradient Green formula Hence identity interpretation intersection irrotational field laplacian Let F line integral magnitude matrix nonzero normal component notation oriented origin orthogonal parallel parallelepiped parametric particle perpendicular point x,y,z position vector proof quaternions radius region right-handed rotation scalar field Show simply connected Solution sphere surface integral tangent tensor triple scalar product unit vector V X F V X G vector analysis vector field vector potential vector product volume integral xy plane zero