Higher Education

Numerical Analysis, 9th Edition

  • Richard L. Burden Youngstown State University
  • J. Douglas Faires
  • ISBN-10: 0538733519  |  ISBN-13: 9780538733519
  • 888 Pages
  • Previous Editions: 2005, 2001, 1997
  • © 2011 | Published
  • College Bookstore Wholesale Price = $221.50
  • Newer Edition Available
  *Why an online review copy?
  • It's the greener, leaner way to review! An online copy cuts down on paper and on time. Reduce the wait (and the weight) of printed texts. Your online copy arrives instantly, and you can review it anytime from your computer or favorite mobile device.

If you prefer a print copy to review, please contact your representative.

About

Overview

This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject.

Features and Benefits

  • Virtually every concept in the text is illustrated by examples, and reinforced by more than 2500 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory.
  • The exercise sets include many applied problems from diverse areas of engineering, as well as from the physical, computer, biological, and social sciences.
  • The algorithms in the text are designed to work with a wide variety of software packages and programming languages, allowing maximum flexibility for users to harness computing power to perform approximations. The book's companion website offers Maple, Mathematica, and MATLAB worksheets, as well as C, FORTRAN, Java, and Pascal programs.
  • The design of the text gives instructors flexibility in choosing topics they wish to cover, selecting the level of theoretical rigor desired, and deciding which applications are most appropriate or interesting for their classes.

Table of Contents

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.
Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software.
2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE.
The Bisection Method. Fixed-Point Iteration. Newton's Method and its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and Müller's Method. Survey of Methods and Software.
3. INTERPOLATION AND POLYNOMIAL APPROXIMATION.
Interpolation and the Lagrange Polynomial. Data Approximation and Neville's Method. Divided Differences. Hermite Interpolation. Cubic Spline Interpolation. Parametric Curves. Survey of Methods and Software.
4. NUMERICAL DIFFERENTIATION AND INTEGRATION.
Numerical Differentiation. Richardson's Extrapolation. Elements of Numerical Integration. Composite Numerical Integration. Romberg Integration. Adaptive Quadrature Methods. Gaussian Quadrature. Multiple Integrals. Improper Integrals. Survey of Methods and Software.
5. INTIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods. Error Control and the Runge-Kutta-Fehlberg Method. Multistep Methods. Variable Step-Size Multistep Methods. Extrapolation Methods. Higher-Order Equations and Systems of Differential Equations. Stability. Stiff Differential Equations. Survey of Methods and Software.
6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS.
Linear Systems of Equations. Pivoting Strategies. Linear Algebra and Matrix Inversion. The Determinant of a Matrix. Matrix Factorization. Special Types of Matrices. Survey of Methods and Software.
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.
Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Iterative Techniques for Solving Linear Systems. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Survey of Methods and Software.
8. APPROXIMATION THEORY.
Discrete Least Squares Approximation. Orthogonal Polynomials and Least Squares Approximation. Chebyshev Polynomials and Economization of Power Series. Rational Function Approximation. Trigonometric Polynomial Approximation. Fast Fourier Transforms. Survey of Methods and Software.
9. APPROXIMATING EIGENVALUES.
Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method. The QR Algorithm. Singular Value Decomposition. Survey of Methods and Software.
10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS.
Fixed Points for Functions of Several Variables. Newton's Method. Quasi-Newton Methods. Steepest Descent Techniques. Homotopy and Continuation Methods. Survey of Methods and Software.
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
The Linear Shooting Method. The Shooting Method for Nonlinear Problems. Finite-Difference Methods for Linear Problems. Finite-Difference Methods for Nonlinear Problems. The Rayleigh-Ritz Method. Survey of Methods and Software.
12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS.
Elliptic Partial Differential Equations. Parabolic Partial Differential Equations. Hyperbolic Partial Differential Equations. An Introduction to the Finite-Element Method.
Survey of Methods and Software.

What's New

  • The treatment of Numerical Linear Algebra is extensively rewritten and expanded, with a new section on Singular Value Decomposition, more material on symmetric and orgothonal matrices, and many new examples and exercises.
  • Examples in the text have been rewritten to better emphasize the problem being solved before the solution is given, and to include computations required for the first steps of iteration processes.
  • A new feature, Illustrations, discusses specific applications of a method outside of the problem-statement-solution format of the Examples.
  • Sections have been expanded and reorganized to make it easier to assign problems directly after material has been presented.
  • The Maple code in the text has been updated to take full advantage of the software's

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Bundle: Text + Student Solutions Manual with Study Guide

ISBN-10: 111169852X | ISBN-13: 9781111698522

List Price = $447.95  | College Bookstore Wholesale Price = $331.75

This Bundle Includes:

  • Numerical Analysis
    List Price = $294.95  | CengageBrain Price = $294.95  | College Bookstore Wholesale Price = $221.50
  • Student Solutions Manual with Study Guide
    List Price = $96.95  | College Bookstore Wholesale Price = $72.75


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Solution Builder  (ISBN-10: 0538735961 | ISBN-13: 9780538735964)

This flexible, personalized online tool lets you easily build and save your own personal solution sets either for printing or posting on password-protected class websites. Complete worked-out solutions are provided for all exercises in the text. Adopting instructors can sign up for access at www.cengage.com/solutionbuilder.

Meet the Author

Author Bio

Richard L. Burden

Richard L. Burden is Emeritus Professor of Mathematics at Youngstown State University. His master's degree in mathematics and doctoral degree in mathematics, with a specialization in numerical analysis, were both awarded by Case Western Reserve University. He also earned a masters degree in computer science from the University of Pittsburgh. His mathematical interests include numerical analysis, numerical linear algebra, and mathematical statistics. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. He was also named a distinguished chair as the chair of the Department of Mathematical and Computer Sciences. He wrote the Actuarial Examinations in Numerical Analysis from 1990 until 1999.

J. Douglas Faires

J. Douglas Faires, late of Youngstown State University, pursued mathematical interests in analysis, numerical analysis, mathematics history, and problem solving. Dr. Faires won numerous awards, including the Outstanding College-University Teacher of Mathematics by the Ohio Section of MAA and five Distinguished Faculty awards from Youngstown State University, which also awarded him an Honorary Doctor of Science award in 2006.