This book is designed for a one- or two-quarter course in continuum mechanics for first-year graduate students and advanced undergraduates in the mathematical and engineering sciences. It was developed, and continually improved, by over four years of teaching of a graduate engineering course (ME 238) at Stanford University, USA, followed by over four years of teaching of an advanced undergraduate mathematics course (MA3G2) at the University of Warwick, UK. The resulting text, we believe, is suitable for use by both applied mathematicians and engineers. Prerequisites include an introductory undergraduate knowledge of linear algebra, multivariable calculus, differential equations and physics.

This book is intended both for use in a classroom and for self-study. Each chapter contains a wealth of exercises, with fully worked solutions to odd-numbered questions. A complete solutions manual is available to instructors upon request. A short bibliography appears at the end of each chapter, pointing to material which underpins, or expands upon, the material discussed here. Throughout the book we have aimed to strike a balance between two classic notational presentations of the subject: coordinate-free notation and index notation. We believe both types of notation are helpful in developing a clear understanding of the subject, and have attempted to use both in the statement, derivation and interpretation of major results. Moreover, we have made a conscious effort to include both types of notation in the exercises.

Chapters 1 and 2 provide necessary background material on tensor algebra and calculus in three-dimensional Euclidean space.