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Scientific Computing with MATLAB and Octave

  • Textbook
  • © 2010

Overview

Authors:
  1. Alfio Quarteroni

    1. Chaire de Modelisation et, Calcul Scientifique (CMCS), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  2. Fausto Saleri

    1. MOX, Politecnico di Milano, Milano, Italy

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  3. Paola Gervasio

    1. , Department of Mathematics, University of Brescia, Brescia, Italy

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  • Offers a combination of problems, algorithms, programs, exercises, illustrations and numerical solutions
  • Includes some 70 examples, 120 solved exercises and 35 Matlab and Octave programs
  • Each chapter opens with representative problems and continues with construction and analysis of algorithms, ad-hoc programs for their implementation
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 2)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XVI
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  2. What can’t be ignored

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 1-40

  3. Nonlinear equations

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 41-74

  4. Approximation of functions and data

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 75-106

  5. Numerical differentiation and integration

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 107-128

  6. Linear systems

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 129-179

  7. Eigenvalues and eigenvectors

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 181-199

  8. Ordinary differential equations

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 201-254

  9. Numerical approximation of boundary-value problems

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 255-302

  10. Solutions of the exercises

    • Alfio Quarteroni, Fausto Saleri, Paola Gervasio
    Pages 303-345

  11. Back Matter

    Pages 347-366
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Keywords

About this book

Preface 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 thatcomputersadoptwhenstoringandoperatingwith realandcomplex 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 raisedthrough exercises and examples, often stemming from s- ci?c applications.

Reviews

From the reviews of the third edition:

“This carefully written textbook is the third English edition and contains substantial new developments on the numerical solution of differential equations. … it is written in a style that is suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject.” (Robert Plato, Zentralblatt MATH, Vol. 1205, 2011)

Authors and Affiliations

  • Chaire de Modelisation et, Calcul Scientifique (CMCS), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Alfio Quarteroni

  • MOX, Politecnico di Milano, Milano, Italy

    Fausto Saleri

  • , Department of Mathematics, University of Brescia, Brescia, Italy

    Paola Gervasio

About the authors

Alfio Quarteroni is Professor and Director of MATHICSE at EPFL, Lausanne (Switzerland), and Professor and Director of MOX at the Politecnico di Milano (Italy). Author of 20 books (mostly published with Springer), and of more than 200 papers, he is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC. Fausto Saleri was Professor of Numerical Analysis at Politecnico di Milano (Italy) until 2007. Author of 11 books published with Springer, he worked on the approximation of partial differential equations, giving important contributions to the study of shallow water equations and to the development of scientific software libraries for finite elements. Paola Gervasio is Associate Professor of Numerical Analysis at University of Brescia (Italy) since 2005. Her research work focuses on the approximation of partial differential equations by spectral methods and domain decomposition techniques.

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