MIT Subject Listing & Schedule
Fall 2023 Search Results

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18.306 Advanced Partial Differential Equations with Applications

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Prereq: (18.03 or 18.032) and (18.04, 18.075, or 18.112)
Units: 3-0-9

Concepts and techniques for partial differential equations, especially nonlinear. Diffusion, dispersion and other phenomena. Initial and boundary value problems. Normal mode analysis, Green's functions, and transforms. Conservation laws, kinematic waves, hyperbolic equations, characteristics shocks, simple waves. Geometrical optics, caustics. Free-boundary problems. Dimensional analysis. Singular perturbation, boundary layers, homogenization. Variational methods. Solitons. Applications from fluid dynamics, materials science, optics, traffic flow, etc.
D. Kouskoulas