With the ever-increasing availability of inexpensive computational aids, numerical analysis has become more accessible and relevant to a wide range of disciplines. This revised second edition provides an introduction to the elementary concepts and methods of numerical analysis. Each main topic is divided into a number of simple and concise steps. The first five are devoted to an important area of errors arising in numerical work with successive steps covering concepts and methods used in the analysis of non-linear equations, systems of linear equations, interpolation, differentiation and integration. Illustrative examples are included at every step and the reader is encouraged to test their immediate comprehension through the use of "checkpoint" questions at the end of the first step. Pseudo-codes for the various algorithms introduced in the steps are included in the appendix and the reader is again encouraged to familiarize themselves with these, as they progess through the text, to gain a full understanding of the programming techniques required. The step-by-step approach in the book, combined with continuous self-assessment, allows the reader to develop at their own pace helping them gain a thorough understanding of numerical analysis that should be useful throughout their course. The book is suitable for first-year mathematics undergraduates, computing, engineering and science students. It should also be a useful text for A Level and college students.

Table of Contents:
Part 1 Errors: sources of error; approximation to numbers; error propagation and generation; floating point arithmetic; approximation to functions. Part 2 Non-linear equations - solving non-linear algebraic and transcendental equations; the bisection methods; method of false position; the methods of simple iteration; the Newton-Raphson interative method. Part 3 Systems of linear equations - solution by elimination; errors and ill-conditioning; the Gauss-Seidel iterative method; matrix inversion; LU decomposition. Part 4 Finite differences - tables; forward, backward and central difference notations; polynominals; detection and correction of mistakes. Part 5 Approximation of functions: linear and quadratic interpolation; Newton interpolation formulae; other interpolation formulae involving finite differences; Lagrange interpolation formulae; divided differences and Aitken's method; inverse interpolation; error bounds. Part 6 Curve fitting. Part 7 Numerical differentiation. Part 8 Numerical integration: the trapezoidal rule; Simpson's rule; quadrature from a table of values; Gauss integration formulae. Part 9 Differential equations.