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Vector Functions of a Single Variable
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angle angular velocity arc length axes axis 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 dx dy dz equals equations Example Exercise expression field F FIGURE Find flow lines flux formula function geometrical given grad f gradient Green formula Green's theorem Hence identity interpretation intersection laplacian Let F line integral line segment magnitude matrix nonzero normal component notation oriented origin orthogonal parallel parametric particle perpendicular point x,y,z position vector potential proof quaternions radius rate of change region right-handed rotation scalar field Show simply connected Solution sphere surface integral tangent Taylor polynomial tensor triple scalar product unit vector vector analysis vector field vector product volume integral xy plane zero