18.306 Advanced Partial Differential Equations with Applications
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.
18.306 will not be offered this semester. It will be available in the Spring semester, and will be instructed by R. R. Rosales.
Lecture occurs 9:30 AM to 11:00 AM on Tuesdays and Thursdays in 2-147.
This class counts for a total of 12 credits.
Scaling, Self-Similarity and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics by Barenblatt, Grigory Isaakovich; Crighton, D. G. (Contribution by); Ablowitz, M. J. (Contribution by); Davis, S. H. (Contribution by); Hinch, E. J. (Contribution by); Iserles, A. (Contribution by); Ockendon, J. (Contribution by); Olver, P. J. (Contribution by)
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