Numerical Methods for Scientific Computing: The Definitive Manual for Math Geeks, 2nd edition

Numerical methods are ubiquitous in scientific research, often working quietly behind the scenes in algorithmic black boxes. Practitioners who use such black boxes don’t always know what’s happening inside them, sometimes leading to inaccurate or inefficient solutions and occasionally flat-out wrong ones. Numerical Methods for Scientific Computing breaks open the algorithms to explain how they work and why they can fail. It helps develop both an intuitive understanding of the underlying mathematical theory and practical skills for research.

This book teaches not only how to be a critical user of scientific computing algorithms but also a knowledgeable creator of them. Ideal as an introductory text for senior undergraduate and first-year graduate students, as a self-study for anyone with a working knowledge of multivariate calculus and linear algebra, and as a modern reference on numerical methods for researchers.

This revised edition, extensively rewritten and expanded, provides a comprehensive guide to using numerical methods in linear algebra, analysis, and differential equations.  This book uses MATLAB for examples and exercises.