This course is an entry-level course in the applied mathematics program. It provides physical backgrounds for classical equations in mathematical physics, including mechanics of fluids, elasticity, viscoelasticity, and complex fluids. These backgrounds are important for students to study analytical theory or numerical computation for partial differential equations. Derivation of these equations and a brief introduction to the corresponding mathematical theory will be given.
The contents include (1) Gas dynamics: thermodynamics, inviscid Euler equations, Riemann problems (2) Fluid mechanics: potential flows, viscosity, Stokes and Navier-Stokes equations, two-phase flows (3) Elasticity: strain, stress, variational formulation, small strain theory, finite elasticity theory (4) Rheology: visco-elasticity (4) Complex fluids: liquid crystals