MATH 640 Partial Differential Equations
Preliminaries from ordinary differential equations, calculus and Lebesgue Integration Theory. Methods of solution of partial differential equations of the first order. Classification of the second order linear partial differential operators. Examples of applied problems leading to hyperbolic, parabolic, and elliptic equations. Cauchy problem. Fredholm alternative in Banach and Hilbert spaces. Properties of potentials. Dirichlet and Neumann problems. Finite difference method. Green's function, separation of variables, and expansion of solutions into eigenfunctions. Prerequisites: 540 and 624.