This text on numerical computing, presented through the medium of the C++ language, is designed for students of science and engineering who are serriously studying nummerical methods for the first time. It should also be of interest to computing scientists who wish to see how C++ can be used in earnest for nummerical computation. The mathematical prerequisites are those which an undergraduate student of science or engineering might be expected to possess after the earlier years of study: elementary calculus, linear algebra, and differential equations. In computing, a good knowledge, such as Basic, Fortran, or Pascal, is asumed, while a working knowledge of C would be an advantage. However, no prior knowledge of C++ is assumed. The language is developed in step with its numerical applications. Features of the language not used here are ignored. What remains, however, is a powerful framework for numerical computations and more than enough for an introductory text.