We developed this text for a sequence of courses on the theory and application of numerical approximation techiques. We designed it primarily for junior-level mathematics, science, and engineering majors who have completed at least the first year   of the standard college calculus sequence. Familiarity with the fundamentals of matrix algebra and differential equations is useful, but we present introductory material on these topics so that such courses need not be prerequisites.

    Previous editions of Numerical Analysis have been used in a wide variety of situations. In some cases, the mathematical analysis underlying the development of approximation techniques was emphasized rather than the methods themselves; in others, the emphasis was reversed. The book has also been used as a core reference for beginning graduate level courses in engineering and computer science programs, and in first-year courses in introductory analysis offered at international universities. We have adapted the book to fit these diverse users without compromising our original purpose:

1. Mathematical Preliminaries and Error Analysis
2. Solutions of Equations in One Variable
3. Interpolation and Polynomial Appoximation
4. Numerical Differentiation and Integration
5. Initial-Value Problema for Ordinary Differential Equations
6. Direct Methods for Solving Linear Systems
7. Iterative Techiques in Matrix Algebra
8. Approximation Theory
9. Appoximating Eigenvalues
10. Numerical Solutions of Nonlinear Systems of Equations
etc.