MATH 6150

Partial Differential Equations

Course Description

Course information provided by the 2025-2026 Catalog.

This course emphasizes the classical aspects of partial differential equations (PDEs) - analytic methods for linear second-order PDEs and first-order nonlinear PDEs - without relying on more modern tools of functional analysis. The usual topics include fundamental solutions for the Laplace/Poisson, heat and and wave equations in Rn, mean-value properties, maximum principles, energy methods, Duhamel's principle, and an introduction to nonlinear first-order equations, including shocks and weak solutions. Additional topics may include Hamilton-Jacobi equations, Euler-Lagrange equations, similarity solutions, transform methods, asymptotics, power series methods, homogenization, distribution theory, and the Fourier transform.

Prerequisites REF-FA25/Corequisites REF-FA25 MATH 4130, MATH 4140, or the equivalent, or permission of instructor. Corequisites: None.

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