## Guide to Scientific ComputingGuide to Scientific Computing provides an introduction to the many problems of scientific computing, as well as the wide variety of methods used for their solution. It is ideal for anyone who needs an understanding of numerical mathematics or scientific computing - whether in mathematics, the sciences, engineering, or economics. This book provides an appreciation of the need for numerical methods for solving different types of problems, and discusses basic approaches. For each of the problems mathematical justification and examples provide both practical evidence and motivations for the reader to follow. Practical justification of the methods is presented through computer examples and exercises. The major effort of programming is removed from the reader, as are the harder parts of analysis, so that the focus is clearly on the basics. Since some algebraic manipulation is unavoidable, it is carefully explained when necessary, especially in the early stages. Guide to Scientific Computing includes an introduction to MATLAB, but the code used is not intended to exemplify sophisticated or robust pieces of software; it is purely illustrative of the methods under discussion. The book has an appendix devoted to the basics of the MATLAB package, its language and programming. The book provides an introduction to this subject which is not, in its combined demands of computing, motivation, manipulation, and analysis, paced such that only the most able can understand. |

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### Contents

Iterative Solution of Equations | 20 |

Approximate Evaluation of Functions | 52 |

Interpolation | 74 |

Numerical Calculus | 119 |

Differential Equations | 171 |

Linear Equations | 210 |

Appendices | 261 |

298 | |

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accuracy Adams-Bashforth method algebra arithmetic binary bisection method bracket Chapter coefficients components convergence CORDIC algorithms corresponding cubic spline cubic spline interpolation curve data points decimal places defined derivative diagonal differential equations divided difference divided difference interpolation eigenvalue error bound error formula error less Euler's method evaluation Example 12 Figure fourth-order Gauss elimination global truncation error graph illustrate implementation initial-value problem interval inverse iteration knots linear equations linear system loop LU factorization mathematical MATLAB commands MATLAB m-file matrix midpoint rule modified Euler method multiplication Newton's method nodes Note number of steps numerical integration obtain operations orthogonal output plot polynomial interpolation quadratic quadrature rule relative error Repeat Exercise result right-hand side roundoff error Runge-Kutta methods secant method second-order Section Simpson's rule slope solve spline interpolation steplength system of linear techniques theorem trapezoid rule tridiagonal system vector yields zero