MATH 8550 - Advanced Partial Differential Equations

3 Credit Hours
Prerequisites: Math 6661 and Math 6265 or equivalent and a background in ordinary differential equations and Matlab or Python programming.
Description
Many natural phenomena have been successfully formulated as partial differential equations: common applications include physics, chemistry, biology, economics and population dynamics. This course will be primarily focused on the theory of partial differential equations such as the heat equation, the Laplace equation, the Poisson equation the wave equation, including separation of variables, Fourier series and transforms, Laplace transforms, and Green’s functions. Some discussion of non-linear conservation laws and the theory of shock waves will be given. The use of computers to solve PDEs numerically (using Matlab or Python) will also be briefly covered.