MATH 425: Numerical Analysis

This course provides an introduction to numerical analysis and its applications in practical problems in applied mathematics and engineering. In most scientific modeling projects, investigators have to deal with very large systems of linear and nonlinear equations. Understanding of which requires powerful computers and a firm understanding of the vast number of existing pertinent algorithms. The main goal of the course is to provide an instruction to algorithmic and mathematical foundations of high-performance scientific computations. Introductory topics of the course include root finding, fixed point methods, interpolation methods, initial value problems and optimization. Particular emphasis will be on optimization methods, including steepest descent, line search methods, newton methods, quasi-Newton methods, trust regions, theory of constraint optimization and linear programming.