This book focuses on the fundamental ideas of continuum mechanics by analyzing models of fluid flow and solid deformation and examining problems in elasticity, water waves, and extremum principles. Mathematics Applied to Continuum Mechanics gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text both for classroom use with upper-division students, and independent study, in the fields of applied mathematics, science and engineering.