Numerical Analysis

What you’ll study

Solutions of equations in one variable: the bisection algorithm, the method of false position, fixed-point iteration, the Newton-Raphson method, error analysis for iterative methods, accelerating the limit of convergence. Interpolation and polynomial approximation: Taylor polynomials, interpolation and Lagrange polynomials, iterated interpolation, extrapolation. Differentiation and integration: numerical differentiation, Richardson's extrapolation, elements of numerical integration, the adaptive quadrature method, Romberg integration, Gaussian quadrature. Solutions of linear systems: pivoting strategies, the LU decomposition method.