1.1 Introduction

This book provides an introduction to numerical analysis and is intended to be used by students of mathematics, engineering, and science. Numerical analysis can be defined as the development and implementation of techniques to find numerical solutions to mathematical problems. It involves engineering and physics in converting a physical phenomenon into a mathematical method; it involves mathematics in developing techniques for the approximate solution of mathematical equations describing the model, and finally it involves computer science for the implementation of these techniques in an optimal fashion for the particular computer available. With the accessibility of computers, it is now possible to get rapid and accurate solutions to many complex problems that create difficulties for the mathematician, engineer, and scientist. In elementary calculus we learned how to differentiate and integrate to get exact answers to a remarkably diverse range of realistic problems that could not be solved by purely algebraic methods. Unfortunately, from a practical point of view, the techniques of elementary (or even advanced) calculus alone are not adequate for solving calculus type problems such as solving polynomial equations of degrees greater than four or even simple equations such as

or to evaluate integrals of type

However, it is impossible to get the exact solutions of these problems. Even when an analytical solution can be found, it may be more theoretical than practical. Fortunately, one rarely needs exact answers. Indeed, in the real world problems themselves are usually inexact because they are generally possessed in terms...