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An Introduction to Scientific Computing

Twelve Computational Projects Solved with MATLAB

  • Textbook
  • © 2007

Overview

Editors:
  1. Ionut Danaila

    1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Pascal Joly

    1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

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    You can also search for this editor in PubMed   Google Scholar

  3. Sidi Mahmoud Kaber

    1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

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  4. Marie Postel

    1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

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  • MATLAB computer programs for each application-project are made available from the Web site of the Editor

  • Versions using the share-ware language Scilab are provided

  • Complementary bibliography is provided with each project

  • Web page for the book: http://www.ann.jussieu.fr/AI2SC provides an introduction to the book, a chapter content and for each chapter compressed archives containing the MATLAB solutions

  • Chapter summaries, detailed illustrations, and study guides at the end of sections included

  • Exericeses and selected solutions provided

  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Numerical Approximation of Model Partial Differential Equations

    Pages 1-32

  3. Nonlinear Differential Equations: Application to Chemical Kinetics

    Pages 33-48

  4. Polynomial Approximation

    Pages 49-83

  5. Solving an Advection-Diffusion Equation by a Finite Element Method

    Pages 85-109

  6. Solving a Differential Equation by a Spectral Method

    Pages 111-125

  7. Signal Processing: Multiresolution Analysis

    Pages 127-150

  8. Elasticity: Elastic Deformation of a Thin Plate

    Pages 151-164

  9. Domain Decomposition Using a Schwarz Method

    Pages 165-191

  10. Geometrical Design: Bézier Curves and Surfaces

    Pages 193-212

  11. Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem

    Pages 213-233

  12. Thermal Engineering: Optimization of an Industrial Furnace

    Pages 235-250

  13. Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations

    Pages 251-284

  14. Back Matter

    Pages 285-294
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Keywords

About this book

Teaching or learning numerical methods in applied mathematics cannot be conceived nowadays without numerical experimentation on computers. There is a vast literature devoted either to theoretical numerical methods or - merical programming of basic algorithms, but there are few texts o?ering a complete discussion of numerical issues involved in the solution of concrete and relatively complex problems. This book is an attempt to ?ll this need. It is our belief that advantages and drawbacks of a numerical method cannot be accounted for without one’s experiencing all the steps of scienti?c comp- ing, from physical and mathematical description of the problem to numerical formulation and programming and, ?nally, to critical discussion of numerical results. The book provides twelve computational projects aimed at numerically solving problems selected to cover a broad spectrum of applications, from ?uid mechanics, chemistry, elasticity, thermal science, computer-aided design, signal and image processing, etc. Even though the main volume of this text concerns the numerical analysis of computational methods and their imp- mentation, we have tried to start, when possible, from realistic problems of practical interest for researchers and engineers. For each project, an introductory record card summarizes the mathem- ical and numerical topics explained and the ?elds of application of the - proach. A level of di?culty, scaling from 1 to 3, is assigned to each project.

Reviews

From the reviews:

"In An Introduction to Scientific Computing, the authors present approaches to the numerical solution of problems drawn from a variety of applications. … This is a graduate-level introduction and the pace is brisk. … This is a strong text on scientific computing for advanced students in applied mathematics. … the book is most appropriate for students with some prior experience in scientific computing … ." (William J. Satzer, MathDL, February, 2007)

"The book is based on material offered by the authors at Universite Pierre et Marie Curie (Paris, France) and different engineering schools. It is intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It may also be used as a reference for researchers and practicing engineers. Since different possible levels of each project are suggested, the text can be used to propose assignments at different graduate levels." (I. N. Katz, Zentralblatt MATH, Vol. 1119 (21), 2007)

"An Introduction to Scientific Computing plunges into solving PDEs by numerical approximation. … the book is an attempt to completely discuss numerical issues for reasonably complex problems at the level of a graduate textbook. A project-based approach is used. … Overall, this is a pleasing and useful companion to more complete expositions of the topic. … If you’re preparing advanced students for a workshop, or organizing a numerical analysis club for the semester, then the book is perfect." (Sorin Mitran, SIAM Review, Vol. 50 (1), 2008)

Editors and Affiliations

  • Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France

    Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel

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