ABSTRACT
This chapter aims to provide a first account of the elements of numerical analysis. When employing numerical methods it is important to distinguish between, and understand the nature of, errors caused by round-off and by approximations used in the method of calculation. Some of the most commonly used numerical methods have been developed for the solution of linear systems of equations. The chapter describes the Gaussian elimination method, the iterative method due to Jacobi and the iterative Gauss–Seidel scheme. It examines elementary interpolation methods and techniques for numerical integration, also known as numerical quadrature and explains the numerical integration of differential equations. Numerical computation and its attendent error are generally inescapable when seeking to solve any moderately complicated problem. On account of this, errors must be understood and, when unavoidable, they must always be controlled.
