AM 213 Numerical Solutions of Differential Equations

Teaches basic numerical methods for numerical linear algebra and, thus, the solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). Covers LU, Cholesky, and QR decompositions; eigenvalue search methods (QR algorithm); singular value decomposition; conjugate gradient method; Runge-Kutta methods; error estimation and error control; finite differences for PDEs; stability, consistency, and convergence. Basic knowledge of computer programming is needed. (Formerly AMS 213.)