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Unformatted text preview: derivative terms in Eq. (5) which does not vanish in curvilinear coordinates shows that atcY/axp are not really the components of a tensor field in general coordinates. A similar situation holds obviously also for tensor fields of higher ranks. See Sec. 2.12 below. When Cartesian coordinates are used, we shall use a comma to denote partial differentiation. Thus, when we restrict ourselves to Cartesian coordinates, +,i, &,j, f f i j , k are ten- sors of rank one, two, three, respectively, provided that 4, &, aij are tensors. Warning: Cartesian tensor equations derived through the use of differ- entiation are in general not valid in curvilinear coordinates. This important point is discussed in the following five sections....
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- Fall '05