This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires 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 students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject.
Mathematical Preliminaries and Error Analysis | Solutions of Equations in One Variable | Interpolation and Polynomial Approximation | Initial-Value Problems for Ordinary Differential Equations | Direct Methods for Solving Linear Systems | Iterative Techniques in Matrix Algebra | Approximation Theory | Approximating Eigenvalues | Numerical Solutions of Nonlinear Systems of Equations | Boundary-Value Problems for Ordinary Differential Equations | Numerical Solutions to Partial Differential Equations
Calculus and Analysis