A practical introduction to numerical methods at an elementary level. Designed to teach the principles of numerical analysis while exposing students to the greatest range of possibilities for scientific computing. Teaches numerical methods that are used in actual numerical software, gives advice on assessing and enhancing accuracy, and shows how problems requiring numerical computation arise in application. Includes 50-page tutorial introduction to Mathematica.
Introduction | Floating-Point Computation | Rootfinding | Systems of Linear Equations | Interpolation | Least-Squares Approximation | Numerical Differentiation and Integration | Ordinary Differential Equations | Overview | Appendix A. Getting Started with Mathematica | Appendix B. Review of Basic Mathematics