Basic Tensor Analysis

Tensors are mathematical objects which ensure that mathematical equations characterizing physics are insensitive to arbitrary choices of a coordinate system. The objective of this chapter is to present a review of tensor analysis using both index and direct notations. To simplify the presentation of tensor calculus, attention is limited to tensors expressed relative to fixed rectangular Cartesian base vectors. (Some of the content in this chapter has been adapted from Rubin (Cosserat theories: shells, rods and points. Springer Science & Business Media, Berlin, 2000) with permission.)