Introduction to continuum mechanics and applications, vectors and indicial notation, tensors, kinematics of a continuum – material and spatial descriptions, displacements, deformations, and strain tensors, compatibility conditions, stress tensors, kinetics of a continuum, conservation and balance laws – conservation of mass, balance of linear and angular momentum, thermodynamic principles, constitutive equations – Cauchy elastic materials, Newtonian fluids, heat transfer, heat conduction laws, constitutive relations for coupled problems, linearized elasticity – governing equations.