This book is based on notes prepared for a senior undergraduate or beginning graduate course that we taught at the universities of Alberta and Victoria. It is primarily intended for use by students of mechanical and civil engineering, but it may be of interest to others. The mathematical background required for the topics covered in the book is modest and should be familiar to senior undergraduate engineering students. In particular it is assumed that a reader has a good knowledge of classical vector mechanics and linear algebra. Also, a background of the classical thermodynamics usually taught in undergraduate engineering courses is desirable. One motivation for the book is to present an introduction to continuum mechanics that requires no background in certain areas of advanced mathematics such as functional analysis and general tensor analysis. The treatment of continuum mechanics is based on Cartesian tensor analysis, but orthogonal curvilinear coordinates and corresponding physical coordinates are considered in appendices.

A list of books that consider tensor analysis and applications is given at the end of chapter 1. Several of the books are out of print but may be useful to students if they can be obtained from libraries. Mathematica is used for symbolic manipulation, numerical computation, and graphs where appropriate, and its use is encouraged.

Chapter 1 is a detailed introduction to Cartesian tensor analysis. It differs from some other treatments of the topic, for example, the early texts by Jeffreys and Temple, by emphasizing both symbolic and suffix notation for first-(vectors) and second-order tensors.