Higher Education

Numerical Methods, 4th, 4th Edition

  • Douglas Faires Youngstown State University
  • Richard L. Burden Youngstown State University
  • ISBN-10: 0495114766  |  ISBN-13: 9780495114765
  • 608 Pages
  • Previous Editions: 2003, 1998, 1993
  • © 2013 | Published
  • College Bookstore Wholesale Price = $291.75
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About

Overview

NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are the same as those covered in the authors' top-selling Numerical Analysis text, but this text provides an overview for students who need to know the methods without having to perform the analysis. This concise approach still includes mathematical justifications, but only when they are necessary to understand the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally.

Features and Benefits

  • Worked examples using computer algebra systems help students understand why the software usually works, why it might fail, and what to do when a software program fails.
  • The exercise sets include problems reflecting a wide range of difficulty as well as problems that offer good illustrations of the methods being discussed, while requiring little calculation.
  • The book contains instructions for a wide range of popular computer algebra systems.
  • This text is designed for use in a one-semester course, but contains more material than needed. Instructors have flexibility in choosing topics and students gain a useful reference for future work.

Table of Contents

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.
Introduction. Review of Calculus. Round-off Error and Computer Arithmetic. Errors in Scientific Computation. Computer Software.
2. SOLUTIONS OF EQUATIONS OF ONE VARIABLE.
Introduction. The Bisection Method. The Secant Method. Newton's Method. Error Analysis and Accelerating Convergence. Müller's Method. Survey of Methods and Software.
3. INTERPOLATION AND POLYNOMIAL APPROXIMATION.
Introduction. Lagrange Polynomials. Divided Differences. Hermite Interpolation. Spline Interpolation. Parametric Curves. Survey of Methods and Software.
4. NUMERICAL INTEGRATION AND DIFFERENTIATION.
Introduction. Basic Quadrature Rules. Composite Quadrature Rules. Romberg Integration. Gaussian Quadrature. Adaptive Quadrature. Multiple Integrals. Improper Integrals. Numerical Differentiation. Survey of Methods and Software.
5. NUMERICAL SOLUTION OF INITIAL-VALUE PROBLEMS.
Introduction. Taylor Methods. Runge-Kutta Methods. Predictor-Corrector Methods. Extrapolation Methods. Adaptive Techniques. Methods for Systems of Equations. Stiff Differentials Equations. Survey of Methods and Software.
6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS.
Introduction. Gaussian Elimination. Pivoting Strategies. Linear Algebra and Matrix Inversion. Matrix Factorization. Techniques for Special Matrices. Survey of Methods and Software.
7. ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS.
Introduction. Convergence of Vectors. Eigenvalues and Eigenvectors. Conjugate Gradient Methods. The Jacobi and Gauss-Seidel Methods. The SOR Method. Error Bounds and Iterative Refinement. Survey of Methods and Software.
8. APPROXIMATION THEORY.
Introduction. Discrete Least Squares Approximation. Continuous Least Squares Approximation. Chebyshev Polynomials. Rational Function Approximation. Trigonometric Polynomial Approximation. Fast Fourier Transforms. Survey of Methods and Software.
9. APPROXIMATING EIGENVALUES.
Introduction. Isolating Eigenvalues. The Power Method. Householder's Method. The QR Method. Survey of Methods and Software.
10. SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS.
Introduction. Newton's Methods for Systems. Quasi-Newton Methods. The Steepest Descent Method. Survey of Methods and Software. Homotopy and Continuation Methods.
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
Introduction. The Linear Shooting Method. Linear Finite Difference Methods. The Nonlinear Shooting Method. Nonlinear Finite-Difference Methods. Variational Techniques. Survey of Methods and Software.
12. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS.
Introduction. Finite-Difference Methods for Elliptic Problems. Finite-Difference Methods for Parabolic Problems. Finite-Difference Methods for Hyperbolic Problems. Introduction to the Finite-Element Method. Survey of Methods and Software.

What's New

  • New examples and exercises appear throughout the text, offering fresh options for assignments.
  • Chapter 7, "Iterative Methods for Solving Linear Systems," includes a new section on Conjugate Gradient Methods.
  • Chapter 10, "Solutions of Systems of Nonlinear Equations," includes a new section on Homotopy and Continuation Methods.
  • Revised techniques for algorithms and programs are included in six languages: FORTRAN, Pascal, C, MAPLE, Mathematica, and MATLAB.
  • All of the Maple material in the text is updated to conform with the newest release (Maple 7). All of the material on the CD that accompanies the book is updated to conform to the latest available versions of Maple, Mathematica, and MATLAB.
  • This edition includes many more examples of Maple code.

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

ISBN-10: 1111652236 | ISBN-13: 9781111652234

List Price = $542.95  | CengageBrain Price = $542.95  | College Bookstore Wholesale Price = $408.00

This Bundle Includes:

  • Numerical Methods, 4th
    List Price = $388.95  | CengageBrain Price = $388.95  | College Bookstore Wholesale Price = $291.75
  • Student Solutions Manual
    List Price = $154.95  | CengageBrain Price = $154.95  | College Bookstore Wholesale Price = $116.25


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: 0495392995 | ISBN-13: 9780495392996)

This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. www.cengage.com/solutionbuilder

Student Solutions Manual  (ISBN-10: 0495392987 | ISBN-13: 9780495392989)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

List Price = $154.95  | CengageBrain Price = $154.95  | College Bookstore Wholesale Price = $116.25

Student Supplements

Student Solutions Manual  (ISBN-10: 0495392987 | ISBN-13: 9780495392989)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives you the information you need to truly understand how these problems are solved.

List Price = $154.95  | CengageBrain Price = $154.95  | College Bookstore Wholesale Price = $116.25

Meet the Author

Author Bio

Douglas Faires

J. Douglas Faires is a Professor of Mathematics at Youngstown State University. His research interests include analysis, numerical analysis, and mathematics history. Dr. Faires has won many awards, including Outstanding College-University Teacher of Mathematics, Ohio Section of MAA (1996) and Youngstown State University, Distinguished Professor for Teaching (1995-1996).

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.