Advertisement

Fundamentals of Scientific Computing

  • Bertil Gustafsson

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 8)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Models and Elementary Mathematics

    1. Front Matter
      Pages 1-1
    2. Bertil Gustafsson
      Pages 3-17
    3. Bertil Gustafsson
      Pages 19-45
    4. Bertil Gustafsson
      Pages 47-65
    5. Bertil Gustafsson
      Pages 67-75
    6. Bertil Gustafsson
      Pages 77-99
  3. Fundamentals in Numerical Analysis

    1. Front Matter
      Pages 101-101
    2. Bertil Gustafsson
      Pages 103-115
    3. Bertil Gustafsson
      Pages 117-123
    4. Bertil Gustafsson
      Pages 125-133
  4. Numerical Methods for Differential Equations

    1. Front Matter
      Pages 135-135
    2. Bertil Gustafsson
      Pages 137-144
    3. Bertil Gustafsson
      Pages 145-171
    4. Bertil Gustafsson
      Pages 173-192
    5. Bertil Gustafsson
      Pages 193-202
  5. Numerical Methods for Algebraic Equations

    1. Front Matter
      Pages 203-203
    2. Bertil Gustafsson
      Pages 205-211
    3. Bertil Gustafsson
      Pages 213-231
  6. Applications

    1. Front Matter
      Pages 233-233
    2. Bertil Gustafsson
      Pages 235-254
    3. Bertil Gustafsson
      Pages 255-262
    4. Bertil Gustafsson
      Pages 263-289
    5. Bertil Gustafsson
      Pages 291-302
    6. Bertil Gustafsson
      Pages 303-304
  7. Bertil Gustafsson
    Pages E1-E1
  8. Back Matter
    Pages 305-322

About this book

Introduction

The book of nature is written in the language of mathematics  -- Galileo Galilei

 

How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built?

The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation.

This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Keywords

computational mathematics computational science and engineering differential equations mathematical models numerical analysis scientific computing

Authors and affiliations

  • Bertil Gustafsson
    • 1
  1. 1., Information TechnologyUppsala UniversityUppsalaSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-19495-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-19494-8
  • Online ISBN 978-3-642-19495-5
  • Series Print ISSN 1611-0994
  • Buy this book on publisher's site