Numerical Methods:

MEE 210A,B,C,D. CSE students must take at least three of these courses. The courses need not be taken in sequence, although it may be advantageous to do so. This course sequence is cross-listed with Math, CS, ECE and CHE. A description follows.

CS/MEE/ECE/MATH 210 Sequence: Numerical Methods in Computational Science and Engineering

Prerequisite: Consent of instructor. Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language.

210A Matrix Analysis and Computation

Graduate level-matrix theory with introduction to matrix computations. SVD's, pseudoinverses, variational characterization of eigenvalues, perturbation theory, direct and iterative methods for matrix computations.

210B Numerical Simulation

Linear multistep methods and Runge-Kutta methods for ordinary differential equations: stability, order and convergence. Stiffness. Differential algebraic equations. Numerical solution of boundary value problems.

210C Numerical Solution of Partial Differential Equations - Finite Difference Methods

Finite difference methods for hyperbolic, parabolic and elliptic PDEs, with application to problems in science and engineering. Convergence, consistency, order and stability of finite difference methods. Dissipation and dispersion. Finite volume methods. Software design and adaptivity.

210D Numerical Solution of Partial Differential Equations - Finite Element Methods

Weighted residual and finite element methods for the solution of hyperbolic, parabolic and elliptic partial differential equations, with application to problems in science and engineering. Error estimates. Standard and discontinuous Galerkin methods.