Let T be a second-order tensor. In terms of its components, T can be expressed as...

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Let T be a second-order tensor. In terms of its components, T can be expressed as T = Tijejej. It has nine (9) components that transform according to the characteristic law 1. Symmetry and Anti-symmetry Let Sij and Aij be second order tensors. Sij is symmetric if Sij = Sji. Ajj is anti-symmetric or skew-symmetric if Aij = - Aji Any second-order tensor can be decomposed into its symmetric and anti-symmetric components, i.e., ;i;j = = ikaji Tkl Its transpose is given by TT = Tjejej. Tij = Sij + Aij where Sij = (Tij + Tji) 2 1 Ay = (TU - TN) Problem 3. Consider the equation u+(X+) grad div u + f = p. (2) where , , p are constants u = u(xi), f = f(x) are vector fields = au t t is the temporal (time) variable Write eq. (2) in indicial and explicit notations. Let T be a second-order tensor. In terms of its components, T can be expressed as T = Tijejej. It has nine (9) components that transform according to the characteristic law 1. Symmetry and Anti-symmetry Let Sij and Aij be second order tensors. Sij is symmetric if Sij = Sji. Ajj is anti-symmetric or skew-symmetric if Aij = - Aji Any second-order tensor can be decomposed into its symmetric and anti-symmetric components, i.e., ;i;j = = ikaji Tkl Its transpose is given by TT = Tjejej. Tij = Sij + Aij where Sij = (Tij + Tji) 2 1 Ay = (TU - TN) Problem 3. Consider the equation u+(X+) grad div u + f = p. (2) where , , p are constants u = u(xi), f = f(x) are vector fields = au t t is the temporal (time) variable Write eq. (2) in indicial and explicit notations.