## Introduction to Precise Numerical MethodsPrecise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. · Clearer, simpler descriptions and explanations ofthe various numerical methods · Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane. |

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### Contents

1 | |

9 | |

3 Classification of Numerical Computation Problems | 25 |

4 RealValued Functions | 37 |

5 Computing Derivatives | 41 |

6 Computing Integrals | 57 |

7 Finding Where a Function fx is Zero | 69 |

8 Finding Roots of Polynomials | 79 |

11 Problems of Linear Programming | 137 |

12 Finding Where Several Functions are Zero | 159 |

13 Optimization Problems | 181 |

14 Ordinary Differential Equations | 191 |

15 Partial Differential Equations | 217 |

16 Numerical Methods with Complex Functions | 235 |

The Precise Numerical Methods Program PNM | 248 |

249 | |

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### Common terms and phrases

array end basic variables boundary calc Call column companion matrix components computation constant container box correct decimal places crossing number defined degree demo program described detA determinant diagonal elements differential equation disks displayed eigenvalues eigenvector elementary function endpoint equal error bound fixed-point decimal places floating-point function fx global error halfwidth higher precision inequality initial value problem integer integral interval arithmetic Jacobian Jordan block Jordan form linear equations linear programming linpro log file mantissa mantissa digits matrix equation midpoint n-square matrix needed negative Newton’s method nonbasic Nonsolvable Problem nonzero notation number of correct obtain operation ordinary differential equations orthant partial derivatives PNM form polynomial power series procedure range arithmetic rational real number rectangle Section series terms simple zero solution representation Solvable Problem solving specified subbox subinterval submatrix Suppose task queue Taylor series Theorem vector