Numerical Methods and Computation. Instructor: Prof. S. R. K. Iyengar, Department of Mathematics, IIT Delhi. This course derives and analyzes numerical methods for the solution of various problems. The course discusses the numerical solution of nonlinear system of algebraic equations. It will construct methods for finding the roots or zeros of a transcendental or a polynomial equation in one variable. Then it will extend the methods for the solution of a system of nonlinear equations. The course will consider a data or a table of values and construct the polynomial that fits this data exactly. This polynomial can be used for interpolating or predicting the value of the function, represent the data at any intermediate point. This polynomial may also be used for various other operations like differentiation and integration. In approximation the course will deal with approximation to a continuous function or to a function which represents the given data. Finally, the course will use the interpolating polynomial of a given data to find the derivative of a function, and construct methods to numerically integrate a given function or to integrate a function that represents a given data.
(from nptel.ac.in)
Lecture 39 - Gauss-Legendre 2-point and 3-point Formula