Numerical Analysis
10th Edition
Published on 1. January 2015
Book
Hardback
912 pages
978-1-305-25366-7 (ISBN)
Description
This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors 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 readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.
More details
Edition
10th edition
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Dimensions
Height: 261 mm
Width: 210 mm
Thickness: 40 mm
Weight
1805 gr
ISBN-13
978-1-305-25366-7 (9781305253667)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.
Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary.
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 Mueller's Method. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
5. INITIAL-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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.
Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
9. APPROXIMATING EIGENVALUES.
Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method. The QR Algorithm. Singular Value Decomposition. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
Bibliography.
Answers to Selected Exercises.
Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary.
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 Mueller's Method. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
5. INITIAL-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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.
Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
9. APPROXIMATING EIGENVALUES.
Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method. The QR Algorithm. Singular Value Decomposition. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
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. Numerical Software and Chapter Summary.
Bibliography.
Answers to Selected Exercises.