Numerical analysis
 Responsibility
 Richard L. Burden, J. Douglas Faires.
 Language
 English.
 Edition
 9th ed.
 Imprint
 Boston, MA : Brooks/Cole, Cengage Learning, c2011.
 Physical description
 xiv, 872 p. : col. ill. ; 26 cm.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA297 .B84 2011  Unknown 
More options
Creators/Contributors
 Author/Creator
 Burden, Richard L.
 Contributor
 Faires, J. Douglas.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 763772) and index.
 Contents

 1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Roundoff Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software. 2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. FixedPoint Iteration. Newton's Method and its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and Muller'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. INITIALVALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of InitialValue Problems. Euler's Method. HigherOrder Taylor Methods. RungeKutta Methods. Error Control and the RungeKuttaFehlberg Method. Multistep Methods. Variable StepSize Multistep Methods. Extrapolation Methods. HigherOrder 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 GaussSiedel 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. QuasiNewton Methods. Steepest Descent Techniques. Homotopy and Continuation Methods. Survey of Methods and Software. 11. BOUNDARYVALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Linear Shooting Method. The Shooting Method for Nonlinear Problems. FiniteDifference Methods for Linear Problems. FiniteDifference Methods for Nonlinear Problems. The RayleighRitz Method. Survey of Methods and Software. 12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS. Elliptic PartialDifferential Equations. Parabolic PartialDifferential Equations. Hyperbolic PartialDifferential Equations. An Introduction to the FiniteElement Method. Survey of Methods and Software.
 (source: Nielsen Book Data)9780538735643 20160607
 Publisher's Summary
 This wellrespected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in reallife situations. In this edition, the presentation has been finetuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded "Numerical Analysis, Third Edition".
(source: Nielsen Book Data)9780538735643 20160607  This wellrespected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one or twosemester 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.
(source: Nielsen Book Data)9780538733519 20160607  Supplemental links
 Table of contents only
Subjects
 Subject
 Numerical analysis.
Bibliographic information
 Publication date
 2011
 ISBN
 9780538733519
 0538733519
 9780538735643
 0538735643