Continuum Mechanics

Continuum mechanics is the unified mathematical language behind almost every deformable thing engineers analyze — a steel beam, a fluid in a pipe, a piece of rubber, soft tissue — all treated as continuous fields rather than discrete particles, with tensor calculus as the grammar that makes the description coordinate-free and physically meaningful. You'll work through problem sets on kinematics of deformation, stress and strain measures, and the balance laws for mass, momentum and energy, then push that machinery into constitutive modeling for solids and fluids, with side trips into linear elasticity, Navier–Stokes, and contact or granular problems. As a graduate-level foundation, it's the course that retroactively explains the assumptions baked into your undergraduate solid mechanics and fluids classes and gives you the framework you'll need before specializing in anything from FEM to soft-matter modeling.