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Partial Differential Equations in Mechanics 1

Fundamentals, Laplace’s Equation, Diffusion Equation, Wave Equation

  • A. P. S. Selvadurai

Table of contents

  1. Front Matter
    Pages I-XIX
  2. A. P. S. Selvadurai
    Pages 1-70
  3. A. P. S. Selvadurai
    Pages 71-85
  4. A. P. S. Selvadurai
    Pages 87-120
  5. A. P. S. Selvadurai
    Pages 121-150
  6. A. P. S. Selvadurai
    Pages 151-234
  7. A. P. S. Selvadurai
    Pages 235-368
  8. A. P. S. Selvadurai
    Pages 369-555
  9. Back Matter
    Pages 557-595

About this book

Introduction

"Por he who knows not mathematics cannot know any other sciences; what is more, he cannot discover his own ignorance or find its proper remedies. " [Opus Majus] Roger Bacon (1214-1294) The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for writing these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universi­ ties. The approach is distinctly different to that wh ich would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling 0/ Problems in Engineering" . An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equations, kinematic constraints, constitutive responses, thermodynamic re­ strictions, etc. , culminates in the development of a partial differential equa­ tion, or sets of partial differential equations, with potential for applications to engineering problems. This ability to distill all the diverse information about a physical or mechanical process into partial differential equations is a particular attraction of the subject area.

Keywords

Applied mechanics Laplace applied mathematics diffusion fluid mechanics model partial differential equation pde solid mechanics verification wave equation waves

Authors and affiliations

  • A. P. S. Selvadurai
    • 1
    • 2
  1. 1.Department of Civil Engineering and Applied MechanicsMcGill UniversityMontrealCanada
  2. 2.Humboldt-Forschungspreisträger, Institut A für MechanikUniversität StuttgartStuttgartGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04006-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08666-3
  • Online ISBN 978-3-662-04006-5
  • Buy this book on publisher's site