This book covers the whole range of numerical mathematics--from linear equations to ordinary differential equations--and details the calculus of errors and partial differential equations. In attempting to give a unified approach of theory, algorithms, applications, and use of software, the book contains many helpful examples and applications. Topics include linear optimization, numerical integration, initial value problems, and nonlinear equations. The book is appearing simultaneously with the problem-solving environment PAN, a system that contains an enlarged hypertext version of the text together with all of the programs described in the book, help systems, and utility tools. (PAN is licensed public domain software.) The text is ideally suited as an introduction to numerical methods and programming for undergraduates in computer science, engineering, and mathematics. It will also be useful to software engineers using NAG libraries and numerical algorithms.