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 both 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 are presented 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. This work 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. It provides short programs in MATLAB that can be used for scientific applications with or without modifications. It is accompanied by a CD-ROM featuring source code, executables, figures, and simulations. It includes an introduction to MATLAB commands, and features an Instructor's Resource Disc for use as a textbook.
1. Number Stytems and Errors
2. Solutions of Nonlinear Equatons
3. Systems of Linear Equations
4. Approximating Functions
5. Differentiation and Integration
6. Ordinary Differential Equations
7. Eigenvalues and Eigenvectors