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Numerical Analysis by J. Douglas Faires, Richard L. Burden and Annette M. Burden
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物品細節
- 物品狀況
- ISBN
- 9781305253667
- Subject Area
- Mathematics
- Publication Name
- Numerical Analysis
- Publisher
- Cengage Learning
- Item Length
- 10.2 in
- Subject
- Numerical Analysis, Mathematical Analysis
- Publication Year
- 2015
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1.5 in
- Features
- Revised
- Item Weight
- 64 Oz
- Item Width
- 8.2 in
- Number of Pages
- 912 Pages
關於產品
Product Identifiers
Publisher
Cengage Learning
ISBN-10
1305253663
ISBN-13
9781305253667
eBay Product ID (ePID)
204245412
Product Key Features
Number of Pages
912 Pages
Language
English
Publication Name
Numerical Analysis
Subject
Numerical Analysis, Mathematical Analysis
Publication Year
2015
Features
Revised
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
1.5 in
Item Weight
64 Oz
Item Length
10.2 in
Item Width
8.2 in
Additional Product Features
Edition Number
10
Intended Audience
College Audience
LCCN
2014-949816
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
518
Edition Description
Revised edition
Table Of 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 Müller'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.
Synopsis
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.
LC Classification Number
QA297.B84 2015
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