## Scientific Computing with MATLAB and OctavePreface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with realand complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from s- ci?c applications. |

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### Contents

Contents | 1 |

Nonlinear equations | 39 |

Approximation of functions and data 71 | 70 |

Numerical differentiation and integration | 101 |

Linear systems | 123 |

Eigenvalues and eigenvectors | 167 |

Ordinary differential equations 187 | 186 |

Numerical methods for initialboundaryvalue | 237 |

Solutions of the exercises | 267 |

References 307 | 306 |

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accurate algorithm allows applied approximation associated assume called Chapter circles coefficients column command complex components composite compute condition consider constant continuous convergence corresponding defined definite denote derivative determinant diagonal differential equations dimension eigenvalues elements equal error estimate Example Exercise exists explicit expression fact factorization Figure finite fixed point formula forward Euler method function function f given graph implemented initial instance instructions integration interpolating interval introduced iterations less linear system MATLAB matrix maximum method converges Newton’s method nodes Note obtained Octave operations parameters polynomial positive possible problem Program quadrature represent requires residual respect result root satisfies solution solve spline square stability step suitable symmetric tends tion tolerance unknown values variable vector verify write zero