An Introduction to Tensor Analysis for Engineers and Applied Scientists

alternating tensor antisymmetric axi axi Cartesian tensors Christoffel symbols considered constant contravariant and covariant contravariant tensor coordinate axes corresponding covariant derivative covariant differentiation defined developed diffusion effects Eijk electromagnetic energy equation 3.4 equation of equation example əxi Əxk Əxl flow follows function generalised coordinate system given heat transfer isotropic isotropic tensors Kronecker delta linear material property metric tensor mixed tensor momentum equation number density obtained parameters particles particular physical processes potential field problems propagation rectangular Cartesian coordinates result scalar potential second order tensor Section shown solid stress tensor stress/strain relationship surface forces symmetrical tensor temperature gradient tensor algebra tensor analysis tensor notation tensor of order tensor quantities term in equation thermal flux thermodynamic transformation rule transport equation turbulent values variables velocity wave written zero аф әт әт әт диі дик ді др дх дхі дхт