MATH 6150 - Partial Differential Equations

Spring. 3 credits. Student option grading.

Prerequisite: MATH 4130, MATH 4140, or the equivalent, or permission of instructor. Offered alternate years.

Staff.

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.