Many physical phenomena of interest in materials science are naturally described by tensors including thermal, mechanical, electrical and magnetic properties. In isotropic materials, many properties (e.g. electrical conductivity) can be described by a single number, a scalar. However in a general crystalline solid, these properties can vary with the direction in which they are measured - and tensors are needed to describe them fully.
This TLP offers an introduction to the mathematics of tensors rather than the intricacies of their applications. Its aims are to familiarise the learner with tensor notation, how they can be constructed and how they can be manipulated to give numerical answers to problems.