Numerical Analysis
Floating point arithmetic; conditioning and stability; numerical linear algebra, including systems of linear equations, least squares, and eigenvalue problems; LU, Cholesky, QR and SVD factorizations; conjugate gradient and Lanczos methods; interpolation by polynomials and cubic splines; Gaussian quadrature. Computer programming assignments form an essential part of the course.This course will cover fundamental methods that are essential for numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments form an essential part of the course. The course will introduce students to numerical methods for (1) nonlinear equations, Newton’s method; (2) ordinary differential equations, Runge-Kutta and multistep methods, convergence and stability; (3) finite difference and ;finite element methods; (4) fast solvers, multigrid method; (5) parabolic and hyperbolic partial differential equations.
