A First Course in Numerical Methods

by Ascher, Uri M.; Greif, Chen

• ISBN13: 9780898719970
• ISBN10: 0898719976
• Format: Paperback
• Copyright: 2011-06-22
• Publisher: SOCIETY FOR INDUSTRIAL & APPLIED MATHEMATICS

Summary

A First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB®, with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science and industrial mathematics.

Table of Contents

List of figures

List of tables

Preface

Numerical algorithms

Roundoff errors

Nonlinear equations in one variable

Linear algebra background

Linear systems: direct methods

Linear least squares problems

Linear systems: iterative methods

Eigenvalues and singular values

Nonlinear systems and optimization

Polynomial interpolation

Piecewise polynomial interpolation

Best approximation

Fourier transform

Numerical differentiation

Numerical integration

Differential equations

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.