Scalars, vectors, and tensors appear in transport theory. For our purposes, only a few definitions relating to tensors and an acquaintance with indicial notation are necessary. We deal with Cartesian tensors, those referred to a right-handed Cartesian coordinate system. A tensor of order zero is a scalar, which is completely defined by its magnitude. A tensor of order one is a vector, which is defined by its magnitude and direction. A tensor of order two is a matrix. Higher order tensors also appear in the transport equations. Tensors may be written in symbolic notation or in indicial notation. Indicial notation displays the indices explicitly and often simplifies the manipulation of equations involving tensors. In this appendix, we present a brief synopsis of indicial notation for Cartesian tensors.

In symbolic notation, we write a vector as V or . Alternatively, we can write a vector in terms of its three components with respect to a right-handed Cartesian coordinate system,

(A1.1a)

The vector is the sum of its three components,

(A1.1b)

where ( ) are the three orthogonal unit vectors. We can write eq. (A1.1b) more compactly by adopting the summation convention, which states that a repeated index is to be summed over its allowed values. With this convention, eq. (A1.1b) becomes

(A1.1c)

We often speak of V _i as a vector, but it should be kept in mind that V _i just represents the three components of the Cartesian vector, V.