Browse: Keyword: Characteristics and Shocks

Abstract:: " The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

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Abstract:: A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.

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