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Advanced Topics in Numerical Analysis: Course Outline (MAT 647)

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

Course Outline

Review of Interpolation formulae, Rational Interpolation, Solution of large system of linear equations: Family of conjugate gradient methods and Multigrid methods for linear systems, Solution of Non-Linear Equations: Theorem on contracting mappings, Bound for Lipschitz constant, Newton’s Method for systems of nonlinear equations, Bairstow’s method. Simultaneous methods, Interpolatory numerical integration for multidimensional case, Brief introduction to finite element and finite volume methods with numerical examples.

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