Introduction to scientific computing

Unique in content and approach, this text covers all the topics that are usually covered in an introduction to scientific computing—but folds in graphics and matrix-vector manipulation in a way that gets students to appreciate the connection between continuous mathematics and computing. Matlab 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theorem—allowing students to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a “hard” problem that involves ill-conditioning, high dimension, etc.; 2) at least one theorem with both a rigorous proof and a “proof by MATLAB” experiment to bolster intuition; 3) at least one recursive algorithm; and 4) at least one connection to a real-world application. The text is brief and clear enough for introductory numerical analysis students to “get their feet wet,” yet comprehensive enough in its treatment of problems and applications for higher-level students to develop a deeper grasp of numerical tools.

Table of Contents

• 1. Power Tools of the Trade.
• 2. Polynomial Interpolation.
• 3. Piecewise Polynomial Interpolation.
• 4. Numerical Integration.
• 5. Matrix Computations.
• 6. Linear Systems.
• 7. The QR and Cholesky Factorizations.
• 8. Nonlinear Equations and Optimization.
• 9. The Initial Value Problem.
• Bibliography.
• Index.