Numerical Analysis with Algorithms and Programming

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equationsInterpolation and approximation of functions by simpler computational building blocks, such as polynomials and splinesThe solution of systems of linear equations and triangularizationApproximation of functions and least square approximationNumerical differentiation and divided differences Numerical quadrature and integrationNumerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs)The text develops students' understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.