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 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 for both classroom use and independent study. This is an ideal text for upper-level undergraduate and graduate students in the fields of applied mathematics, science, and engineering. Foreword to the Classics Edition; Preface; Contents; Conventions; Part A: Geometrical Prerequisites for Three-Dimensional Continuum Mechanics; Chapter 1: Vectors, Determinants, and Motivation for Tensors; Chapter 2: Cartesian Tensors; Part B: Problems in Continuum Mechanics; Chapter 3: Viscous Fluids; Chapter 4: Foundations of Elasticity; Chapter 5: Some Examples of Static Problems in Elasticity; Chapter 6: Introduction to Dynamic Problems in Elasticity; Part C: Water Waves; Chapter 7: Formulation of the Theory of Surface Waves in an Inviscid Fluid; Chapter 8: Solution in the Linear Theory; Chapter 9: Group Speed and Group Velocity; Chapter 10: Nonlinear Effects; Part D: Variational Methods and Extremum Principles; Chapter 11: Calculus of Variations; Chapter 12: Characterization of Eigenvalues and Equilibrium States as Extrema; Bibliography; Hints and Answers; Index.