## Elementary Theory and Application of Numerical AnalysisConcise, rigorous introduction to modern numerical analysis, especially error-analysis aspects of problems and algorithms discussed. Aimed primarily at sophomore- and junior-level engineering and physical sciences majors, book focuses on a small number of basic concepts and techniques, emphasizing why each works. Exercises and answers. |

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### Contents

MATRIX COMPUTATIONS AND SOLUTION | 32 |

ITERATIVE SOLUTION OF SYSTEMS | 65 |

ERRORS AND FLOATINGPOINT ARITHMETIC | 141 |

NUMERICAL DIFFERENTIATION | 166 |

INTRODUCTION TO THE NUMERICAL SOLUTION | 208 |

NUMERICAL SOLUTION OF ORDINARY | 246 |

279 | |

INDEX m | 303 |

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### Common terms and phrases

ahout ahove ahsolute value Algorithm 3-1 Apply approximate value arhitrary calculation Chap coefficients column continuous convergence defined DEFINITION derivatives diagonal differential equations digits discussed elements error hound Euler's method exact solution Example Exercise 29 exists Find a hound first-order ODE fixed-point iteration floating-point arithmetic FORTRAN program function given helow given hy gives hased hecause Hence hetween Heun's method hoth hounded hy hy Algorithm illustrate inherent error integration interval inverse linear equations linear interpolation linear system Lipschitx condition mantissa mathematical neighhorhood Newton-Raphson iteration notation numerical analysis numerical differentiation numerical solution ohtained possihle prohlem proof Prove real numhers remainder result Rolle's theorem round-off error Runge-Kutta Runge-Kutta method satisfies a Lipschitx Simpson's rule solving starting values suhstitution Suppose system AX system of first-order tahle Taylor algorithm theory tion trapexoidal rule truncation error unique solution variahle Write a FORTRAN xero xt,h y(xt