Numerical Analysis

This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers intuition, and demonstrate the subjects practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burdens NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject. Table of Contents 1 Mathematical Preliminaries and Error Analysis 2 Solutions of Equations in One Variable 3 Interpolation and Polynomial Approximation 4 Numerical Differentiation and Integration 5 Initial-Value Problems for Ordinary Differential Equations 6 Direct Methods for Solving Linear Systems 7 Iterative Techniques in Matrix Algebra 8 Approximation Theory 9 Approximating Eigenvalues 10 Numerical Solutions of Nonlinear Systems of Equations 11 Boundary-Value Problems for Ordinary Differential Equations 12 Numerical Solutions to Partial Differential Equations