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Essential Partial Differential Equations

Analytical and Computational Aspects

  • David F. Griffiths
  • John W. Dold
  • David J. Silvester

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 1-9
  3. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 11-25
  4. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 27-36
  5. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 37-57
  6. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 59-83
  7. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 85-118
  8. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 119-128
  9. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 129-159
  10. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 161-194
  11. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 195-235
  12. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 237-274
  13. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 275-317
  14. David F. Griffiths, John W. Dold, David J. Silvester
    Pages 319-332
  15. Back Matter
    Pages 333-368

About this book

Introduction

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.
 
Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.
 
The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors.
 
Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific an

d engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.

Keywords

Discrete Fourier Analysis Energy Methods Finite Difference Approximation Maximum Principles Method of Characteristics Nonlinear Partial Differential Equations Origin of PDEs

Authors and affiliations

  • David F. Griffiths
    • 1
  • John W. Dold
    • 2
  • David J. Silvester
    • 3
  1. 1.University of DundeeFifeUnited Kingdom
  2. 2.School of MathematicsThe University of ManchesterManchesterUnited Kingdom
  3. 3.School of MathematicsThe University of ManchesterManchesterUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22569-2
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-22568-5
  • Online ISBN 978-3-319-22569-2
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site