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Vector Functions of a Single Variable
Line Surface and Volume Integrals
6 other sections not shown
A X B angle angular velocity arc length axis component of F compute 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 equation example exercise expression field F figure Find flow lines fluid flux force formula function geometrical given grad gradient Green formula Green's theorem Hence identity interpretation intersection irrotational field laplacian Let F line integral magnitude matrix nonzero normal component notation oriented origin orthogonal parallel parametric particle perpendicular position vector proof quaternions radius region right-handed rotation scalar field Show simply connected Solution sphere surface integral tangent tensor transformation triple scalar product unit vector V X F V X G vector analysis vector field vector potential vector product Verify volume integral xy plane zero