Advanced Differential Equations: Partial Differential Equations - 625.717

This course presents practical methods for solving partial differential equations (PDEs). The course covers solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables. Topics include Fourier series, separation of variables, existence and uniqueness theory for general higher-order equations, eigenfunction expansions, numerical methods, Green’s functions, and transform methods. MATLAB, a high-level computing language, is used in the course to complement the analytical approach and to motivate numerical methods.

Course Prerequisite(s)

EN.625.604 Ordinary Differential Equations or equivalent graduate-level ODE class and knowledge of eigenvalues and eigenvectors from matrix theory. (Note: The standard undergraduate-level ODE class alone is not sufficient to meet the prerequisites for this class.)