Integration and Differentiation

In many cases analytical integration is not possible e.g. if we are given function data already sampled in discrete points or we have a function but there is no closed form solution (primitive function). Some times it is not practical e.g. because the primitive function would be too large or complicated to derive, represent or evaluate. In either case numerical integration called {\em quadrature} can be used to find a numerical value for a definite integral. A numerical quadrature rule is a weighted sum of finite number of sample values of integrand function. Main issues are: Lecures cover: Method of undetermined coefficients, Newton-Cotes rules, Error estimation, Gaussian quadrature, finite difference approximation to derivatives.