Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."
—Zentrablatt Math
". . . carefully structured with many detailed worked examples . . ."
—The Mathematical Gazette
". . . an up-to-date and user-friendly account . . ."
—Mathematika
An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics.
A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth.
The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Table of Contents:
Introductory concepts and calculus review A survey of simple methods and tools
Root-finding
Interpolation and approximation
Numerical integration
Numerical methods for ordinary differential equations
Numerical methods for the solution of systems of equations
Approximate solution of the algebraic eigenvalaue problem
A survey of finite difference methods for partial differential equations
Appendix A. Proofs of selected theorems, and other additional material
