An Introduction to Numerical Methods and Analysis, Solutions Manual

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.

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

James F. Epperson, PhD, is Associate Editor of Mathematical Reviews for the American Mathematical Society. He was previously Associate Professor?in the Department of Mathematical Sciences at the University of Alabama in Huntsville. Dr. Epperson received his PhD from Carnegie-Mellon University in 1980. His research interests include the numerical solution of nonlinear evolution equations via finite element and finite difference methods, including error estimates; the use of kernel functions to solve evolution equations; and numerical methods in mathematical finance.