Floating point arithmetic; numerical solution of ODEs; finite difference methods for PDEs; stability, accuracy and convergence: von Neumann analysis, CFL condition, Lax Theorem. Finite element methods: boundary value problems and elliptic PDEs. Spectral and pseudo-spectral methods. Prerequisite(s): MATH 2454 and MATH 3806, or permission of the School.Also offered at the graduate level, with different requirements, as MATH 5806, for which additional credit is precluded.Lectures three hours a week.