In this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods. This text, suitable for advanced undergraduate and graduate-level courses, supplies the required knowledge not just by listing and describing methods, but by analyzing them carefully and stressing techniques for developing new methods. Based on each author's more than 40 years of experience in teaching university courses, this book offers lucid, carefully presented coverage of norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, numerical solution of differential equations, and more. No mathematical preparation beyond advanced calculus and elementary linear algebra (or matrix theory) is assumed. Examples and problems are given that extend or amplify the analysis in many cases.