Numerical Methods

This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally.

Ch1. Mathematical Preliminaries and Error AnalysisCh2. Solutions of Equations of One VariableCh3. Interpolation and Polynomial ApproximationCh4. Numerical Integration and Differentiation Ch5. Numerical Solution of Initial-value Problems Ch6. Direct Methods for Solving Liner Systems Ch7. Iterative Methods for Solving Linear Systems Ch8. Approximation Theory Ch9. Approximating Eigen values Ch10. Solutions of Systems of Nonlinear Equations Ch11. Boundary-value Problems for Ordinary Differential Ch12. Numerical Methods for Partial Differential Equations