## Introduction to Algorithms and Numerical Methods |

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### Contents

SOLUTION OF SINGLE EQUATIONS | 2-1 |

NUMERICAL APPROXIMATION | 3-1 |

NUMERICAL INTEGRATION | 4-1 |

Copyright | |

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### Common terms and phrases

ALGORITHMS AND NUMERICAL approximation arguments assumed augmented matrix base points coefficients column Computer Output condenser constant convergence corresponding data set derivative elements equa1-interval search equal-interval error term Euler's method evaluated example f(xQ flow diagram FORMAT FORTRAN FREQ function f(x functional values given golden section search initial INPUT DATA integration formula interpolating polynomial interval of uncertainty INTRODUCTION TO ALGORITHMS involved ITRUE JMAX linear interpolation LMBDA1 main program molal mole Moody friction factor Newton's method Note NUMERICAL METHODS O.IE objective function obtained optimization pivot Pn(x pressure problem procedure Program Listing QTOT repeated applications root Runge-Kutta Runge-Kutta methods SDATA Section sequence shown in Fig Simpson's rule simultaneous equations solving starting interval statement step subscripts successive substitutions Suggested test data techniques temperature TLULIN trapezoidal rule truncation error TSTAR upper limit variables vector viscosity Write a program XVAL zero