Computer mathematics II

This course is divided into nine lectures. The first lecture seeks to justifies the use of numerical methods as opposed to algebraic methods for some types of mathematical computations. It also explains types of errors and strategies of reducing them. The second and third lectures describes a total of four numerical methods that can be used to estimate the roots of non linear continuous function. The relative merits of each method are also discussed.

In the fourth and fifth lectures we first revise the concepts of differentiation and integration of functions. We develop analytic methods of differentiation and integration and apply them to simple functions. We then discuss numerical methods of finding the value of the derivative of a function at a point, and finding the definite integral of a continuous function over an interval on the real line. Lecture six revises the study of matrices. It deals with the arithmetic of matrices and use of matrices in solving systems of linear equations analytically.

In lectures seven and eight, numerical methods for solving systems of linear equations are explained. A direct method and two iterative schemes are described. Lecture nine introduces the student to two approaches that can be used to perform interpolation in continuous non linear functions.