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Numerical Analysis Ninth Edition by Richard L. Burden and J. Douglas Faires

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Numerical Analysis Ninth Edition written by Richard L. Burden, Youngstown State University and J. Douglas Faires, Youngstown State University . This is an other book of mathematics cover the following topics.

  • 1 Mathematical Preliminaries and Error Analysis
    1.1 Review of Calculus
    1.2 Round-off Errors and Computer Arithmetic
    1.3 Algorithms and Convergence
    1.4 Numerical Software

  • 2 Solutions of Equations in One Variable
    2.1 The Bisection Method
    2.2 Fixed-Point Iteration
    2.3 Newton’s Method and Its Extensions
    2.4 Error Analysis for Iterative Methods
    2.5 Accelerating Convergence
    2.6 Zeros of Polynomials and Müller’s Method
    2.7 Survey of Methods and Software

  • 3 Interpolation and Polynomial Approximation
    3.1 Interpolation and the Lagrange Polynomial
    3.2 Data Approximation and Neville’s Method
    3.3 Divided Differences
    3.4 Hermite Interpolation
    3.5 Cubic Spline Interpolation
    3.6 Parametric Curves
    3.7 Survey of Methods and Software

  • 4 Numerical Differentiation and Integration
    4.1 Numerical Differentiation
    4.2 Richardson’s Extrapolation
    4.3 Elements of Numerical Integration
    4.4 Composite Numerical Integration
    4.5 Romberg Integration
    4.6 Adaptive Quadrature Methods
    4.7 Gaussian Quadrature
    4.8 Multiple Integrals
    4.9 Improper Integrals
    4.10 Survey of Methods and Software

  • 5 Initial-Value Problems for Ordinary Differential Equations
    5.1 The Elementary Theory of Initial-Value Problems
    5.2 Euler’s Method
    5.3 Higher-Order Taylor Methods
    5.4 Runge-Kutta Methods
    5.5 Error Control and the Runge-Kutta-Fehlberg Method
    5.6 Multistep Methods
    5.7 Variable Step-Size Multistep Methods
    5.8 Extrapolation Methods
    5.9 Higher-Order Equations and Systems of Differential Equations
    5.10 Stability
    5.11 Stiff Differential Equations
    5.12 Survey of Methods and Software

  • 6 Direct Methods for Solving Linear Systems
    6.1 Linear Systems of Equations
    6.2 Pivoting Strategies
    6.3 Linear Algebra and Matrix Inversion
    6.4 The Determinant of a Matrix
    6.5 Matrix Factorization
    6.6 Special Types of Matrices
    6.7 Survey of Methods and Software

  • 7 IterativeTechniques in Matrix Algebra
    7.1 Norms of Vectors and Matrices
    7.2 Eigenvalues and Eigenvectors
    7.3 The Jacobi and Gauss-Siedel Iterative Techniques
    7.4 Relaxation Techniques for Solving Linear Systems
    7.5 Error Bounds and Iterative Refinement
    7.6 The Conjugate Gradient Method
    7.7 Survey of Methods and Software

  • 8 ApproximationTheory
    8.1 Discrete Least Squares Approximation
    8.2 Orthogonal Polynomials and Least Squares Approximation
    8.3 Chebyshev Polynomials and Economization of Power Series
    8.4 Rational Function Approximation
    8.5 Trigonometric Polynomial Approximation
    8.6 Fast Fourier Transforms
    8.7 Survey of Methods and Software

  • 9 Approximating Eigenvalues
    9.1 Linear Algebra and Eigenvalues
    9.2 Orthogonal Matrices and Similarity Transformations
    9.3 The Power Method
    9.4 Householder’s Method
    9.5 The QR Algorithm
    9.6 Singular Value Decomposition
    9.7 Survey of Methods and Software

  • 10 Numerical Solutions of Nonlinear Systems of Equations
    10.1 Fixed Points for Functions of Several Variables
    10.2 Newton’s Method
    10.3 Quasi-Newton Methods
    10.4 Steepest Descent Techniques
    10.5 Homotopy and Continuation Methods
    10.6 Survey of Methods and Software

  • 11 Boundary-Value Problems for Ordinary Differential Equations
    11.1 The Linear Shooting Method
    11.2 The Shooting Method for Nonlinear Problems
    11.3 Finite-Difference Methods for Linear Problems
    11.4 Finite-Difference Methods for Nonlinear Problems
    11.5 The Rayleigh-Ritz Method
    11.6 Survey of Methods and Software

  • 12 Numerical Solutions to Partial Differential Equations
    12.1 Elliptic Partial Differential Equations
    12.2 Parabolic Partial Differential Equations
    12.3 Hyperbolic Partial Differential Equations
    12.4 An Introduction to the Finite-Element Method
    12.5 Survey of Methods and Software

  • Bibliography

  • Answers to Selected Exercises

  • Index

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