Description
Numerical Analysis presents the theory and application of numerical approximation techniques, with an emphasis on understanding how, why, and when numerical methods work and how errors affect their results. The book begins with mathematical preliminaries, round-off errors, computer arithmetic, algorithms, and convergence, then develops methods for solving equations in one variable, interpolation and polynomial approximation, and numerical differentiation and integration. It also covers numerical methods for initial-value and boundary-value problems in ordinary differential equations, direct and iterative techniques for solving linear systems, approximation theory, eigenvalue computation, and nonlinear systems of equations. The final chapters introduce numerical methods for partial differential equations, including elliptic, parabolic, and hyperbolic problems and an introduction to the finite-element method. Through examples, exercises, numerical software, and applications in mathematics, computing, engineering, and physical sciences, the book provides a comprehensive foundation in numerical analysis.
