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Numerical Analysis 9th Edition

Richard L. Burden, J. Douglas Faires

  • Published
  • Previous Editions 2005, 2001, 1997
  • 888 Pages

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.

Richard L. Burden, Youngstown State University

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.
  • 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
  • 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.
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.

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  • ISBN-10: 1133384609
  • ISBN-13: 9781133384601
  • STARTING AT $23.49

  • STARTING AT $47.49

  • ISBN-10: 0538733519
  • ISBN-13: 9780538733519
  • Bookstore Wholesale Price $225.00
  • RETAIL $299.95

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

FOR INSTRUCTORS

Student Solutions Manual with Study Guide

ISBN: 9781305253674
This manual contains worked-out solutions to many of the problems in the text. For the complete manual, go to www.cengagebrain.com/.

FOR STUDENTS

Student Solutions Manual with Study Guide

ISBN: 9781305253674
This manual contains worked-out solutions to many of the problems in the text. For the complete manual, go to www.cengagebrain.com/.