Numerical Methods

Abstract

So far we have been almost entirely concerned with problems that have exact analytical solutions. The only exception was in the case of infinite series where we had to consider the question of convergence. In our numerical work we have used small numbers so that the arithmetic has been easy. However, problems in real life are not always so easy. For example, in chapter 3 we indicated that many functions cannot be integrated analytically. For such problems it is necessary to adopt numerical methods. Numerical analysis is a large subject and in this chapter we can only give a brief introduction to a few numerical procedures. We concentrate on the ideas behind the methods and ignore error analysis. The particular methods discussed are not necessarily those that would be used in practice for serious computation. For a thorough discussion the student should consult a text on numerical analysis such as McCracken and Dorn, 1964.