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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Alfio Quarteroni; Fausto Saleri |

ISBN: | 9783642593390 3642593399 |

OCLC Number: | 851759961 |

Description: | 1 online resource (ix, 257 pages). |

Contents: | 1. What can't be ignored -- 1.1 Real numbers -- 1.2 Complex numbers -- 1.3 Matrices -- 1.4 Real functions -- 1.5 To err is not only human -- 1.6 A few more words about MATLAB -- 1.7 What we haven't told you -- 1.8 Exercises -- 2. Nonlinear equations -- 2.1 The bisection method -- 2.2 The Newton method -- 2.3 Fixed point iterations -- 2.4 What we haven't told you -- 2.5 Exercises -- 3. Approximation of functions and data -- 3.1 Interpolation -- 3.2 Piecewise linear interpolation -- 3.3 Approximation by spline functions -- 3.4 The least squares method -- 3.5 What we haven't told you -- 3.6 Exercises -- 4. Numerical differentiation and integration -- 4.1 Approximation of function derivatives -- 4.2 Numerical integration -- 4.3 Simpson adaptive formula -- 4.4 What we haven't told you -- 4.5 Exercises -- 5. Linear systems -- 5.1 The LU factorization method -- 5.2 The technique of pivoting -- 5.3 How accurate is the LU factorization? -- 5.4 How to solve a tridiagonal system -- 5.5 Iterative methods -- 5.5.1 How to construct an iterative method -- 5.6 When should an iterative method be stopped? -- 5.7 Richardson method -- 5.8 What we haven't told you -- 5.9 Exercises -- 6. Eigenvalues and eigenvectors -- 6.1 The power method -- 6.2 Generalization of the power method -- 6.3 How to compute the shift -- 6.4 Computation of all the eigenvalues -- 6.5 What we haven't told you -- 6.6 Exercises -- 7. Ordinary differential equations -- 7.1 The Cauchy problem -- 7.2 Euler methods -- 7.3 The Crank-Nicolson method -- 7.4 Zero-stability -- 7.5 Stability on unbounded intervals -- 7.6 High order methods -- 7.7 The predictor-corrector methods -- 7.8 Systems of differential equations -- 7.9 What we haven't told you -- 7.10 Exercises -- 8. Numerical methods for boundary-value problems -- 8.1 Approximation of boundary-value problems -- 8.2 Finite differences in 2 dimensions -- 8.3 What we haven't told you -- 8.4 Exercises -- 9. Solutions of the exercises -- 9.1 Chapter 1 -- 9.2 Chapter 2 -- 9.3 Chapter 3 -- 9.4 Chapter 4 -- 9.5 Chapter 5 -- 9.6 Chapter 6 -- 9.7 Chapter 7 -- 9.8 Chapter 8 -- Index of MATLAB Programs. |

Series Title: | Texts in computational science and engineering, 2. |

Responsibility: | by Alfio Quarteroni, Fausto Saleri. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "Can be used either as a complement to a basic or more advanced course in numerical analysis, or as a do-book for a short and practical introduction to the subject ... . closing section of each chapter is a list of exercises, adapted to the level of the reader. ... exercises are essential because the emphasis is clearly on the practical implementation ... . after working through this book, the reader is brought to a relatively experienced lower step up the ladder of scientific computing." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008) Read more...

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