Introduction to Numerical Analysis Using MATLAB

Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for courses in numerical analysis and as a reference for practicing engineers and scientists, this book presents the theoretical concepts of numerical analysis and the practical justification of these methods through computer examples with the latest version of MATLAB. The book addresses a variety of questions ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations, with particular emphasis on the stability, accuracy, efficiency and reliability of numerical algorithms. The CD-ROM which accompanies the book includes source code, a numerical toolbox, executables, and simulations. FEATURES*Presents each numerical method by first providing examples and geometric motivation, then the steps to perform the computation, and finally the mathematical derivation of the process *Provides short programs in MATLAB that can be used for scientific applications with or without modifications *Shows the visual representation of mathematical concepts in 2D graphics and is compatible with the current MATLAB v.7.5. *Accompanied by a CD-ROM featuring source code, executables, figures, and simulations *Includes an introduction to MATLAB commands *Features an Instructor s Resource Disc for use as a textbook BRIEF TABLE OF CONTENTS 1. Number Systems and Errors. 2. Nonlinear Equations. 3. Systems of Linear Equations. 4. Approximating Functions. 5. Numerical Differentiation and Integration. 6. Ordinary Differential Equations. 7. The Eigenvalue problems. Appendix A. Mathematical Preliminaries. B. Introduction to MATLAB.