This book is designed for an introductory course in numerical methods for students of engineering and science at universities and colleges of advanced education. It is an outgrowth of a course of lectures and tutorials (problem- solving sessions) which the author has given for a number of years at the University of New South Wales and elsewhere. The course is normally taught at the rate of 1i hours per week throughout an academic year (28 weeks). It has occasionally been given at double this rate over half the year, but it was found that students had insufficient time to absorb the material and experiment with the methods. The material presented here is rather more than has been taught in anyone year, although all of it has been taught at some time. The book is concerned with the application of numerical methods to the solution of equations - algebraic, transcendental and differential - which will be encountered by students during their training and their careers. The theoretical foundation for the methods is not rigorously covered. Engineers and applied scientists (but not, of course, mathematicians) are more con- cerned with using methods than with proving that they can be used. However, they 'must be satisfied that the methods are fit to be used, and it is hoped that students will perform sufficient numerical experiments to con- vince themselves of this without the need for more than the minimum of theory which is presented here.