This new book from the authors of the highly successful classic Numerical Methods (Prentice-Hall, 1974) addresses the increasingly important role of numerical methods in science and engineering. It is more cohesive and comprehensive than any other modern textbook in the field. While treating traditional and well-developed topics, it also emphasizes concepts and ideas of importance to the design of accurate and efficient algorithms with applications to scientific computing. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume.