## Numerical AnalysisThis 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. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |

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page 206 bisection method

### Contents

Mathematical Preliminaries and Error Analysis ... | 1 |

Solutions of Equations in One Variable | 47 |

Interpolation and Polynomial Approximation ... | 105 |

Numerical Differentiation and Integration ... | 173 |

InitialValue Problems for Ordinary Differential Equations ... | 259 |

Direct Methods for Solving Linear Systems ... | 357 |

Iterative Techniques in Matrix Algebra | 431 |

Approximation Theory | 497 |

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2010 C'enguae Learning 2010 Cengage Learning actual error Algorithm approximate the solution boundary-value problem coefficients compute convergence copied Copyright 2010 C'enguae Copyright 2010 Cengage cubic spline defined derivative determine diagonal differential equation Due to electronic duplicated eBook and/or eChapter(s eigenvalues eigenvectors electronic rights endpoints entries error bound Euler’s method evaluations Example Exercise Set formula function Gaussian elimination given gives implies initial approximation initial-value problems integral interpolating polynomial interval least squares linear system Maple matrix Newton’s method nodes nonlinear norm number of iterations obtained orthogonal OUTPUT polynomial of degree positive definite procedure quadrature Repeat Exercise requires Rights Reserved round-off error Runge-Kutta method scanned Secant method Section sequence Show Simpson’s rule sinx solve Step Suppose suppressed Table Taylor polynomial technique Theorem third party content truncation error values vector whole wi+1 y(ti zero