Math 721/821- Math 722/822. Advanced Applied Numerical Methods I & II. Lecture 3 hours; 3 credits each semester.  Prerequisite: Math 622. Numerical methods applied to both partial differential equations and integral equations.  For PDEs, the finite difference method, the finite element method and the boundary element method are studied. A priori and a posteriori error estimates are examined. For integral equations, topics include Galerkin method, collocation method and Petrov-Galerkin method. This course is designated as a simulation course.