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The Concept of Scalar and Vector Fields
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approaches zero becomes Cartesian coordinate system Chapter component consider constant coordinate variables curl F cylindrical coordinate system defined determine differential discussion div F ds(R dt dt dV(R element of length example field F field lines Figure finite flux function given grad h gradient Green's theorem integrand intersection irrotational Laplace equation Laplacian line integral located magnitude normal observation point obtain orthogonal path periphery physical point in space Poisson equation position vector rate of change region of space represents result rotation scalar and vector scalar field scalar potential scalar source sense shown in Fig side of Eq solid angle space curve specified sphere spherical coordinate system Stokes's theorem surface element surface integral three-dimensional transformation two-dimensional unit vector uR_R vector field vector potential vector product vector quantity volume write Eq written