Principles of Continuum Applied Mathematics
MIT OpenCourseWare's 18.311 covers the mathematics of continuous physical systems, drawing examples from traffic flow, fluid motion, elasticity, and granular flows. Topics include the continuum limit, conservation laws, quasi-equilibrium behavior, kinematic waves, characteristics, simple waves and shocks, and linear and nonlinear diffusion. The course also treats numerical solution of wave equations, finite differences, consistency and stability, discrete and fast Fourier transforms, spectral methods, and Fourier and Laplace transforms and series. Additional topics can include sonic booms, Mach cones, caustics, lattices, dispersion, and group velocity. Materials come from MIT's OpenCourseWare archive under a Creative Commons license, including lecture notes and problem sets typical of the department's applied math sequence. No certificate is offered, since OCW is a free self-study archive rather than an instructor-led platform.