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VECTOR FUNCTIONS OF A SINGLE VARIABLE
SCALAR AND VECTOR FIELDS
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angle angular velocity arc length axes axis charge closed curve component of F compute conservative constant coordinate curves coordinate system curl F curvilinear coordinates cylindrical coordinates defined denote density derivative differentiable directed line segment div F divergence theorem domain dt dt dx dy equals equations Example Exercise expression field F FIGURE Find flow lines flux formula function geometrical given gradient Green's theorem Hence identity interpretation intersection isotimic surfaces Let F line integral magnitude matrix nonzero normal component oriented origin orthogonal parallel parallelepiped parametric perpendicular point in space point x,y,z position vector potential proof quaternions radius rate of change region represented rotation scalar field Show simply connected Solution spherical coordinates surface integral tangent tangential component transformation triple scalar product unit vector vector analysis vector field vector product volume integral xy plane zero