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Partial Differential Equations

Mathematical Techniques for Engineers

  • Marcelo Epstein

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Background

    1. Front Matter
      Pages 1-1
    2. Marcelo Epstein
      Pages 25-47
  3. The First-Order Equation

    1. Front Matter
      Pages 49-49
    2. Marcelo Epstein
      Pages 51-74
    3. Marcelo Epstein
      Pages 75-88
    4. Marcelo Epstein
      Pages 89-112
  4. Classification of Equations and Systems

    1. Front Matter
      Pages 113-113
    2. Marcelo Epstein
      Pages 115-130
    3. Marcelo Epstein
      Pages 131-153
  5. Paradigmatic Equations

    1. Front Matter
      Pages 155-155
    2. Marcelo Epstein
      Pages 157-182
    3. Marcelo Epstein
      Pages 183-208
    4. Marcelo Epstein
      Pages 209-238
    5. Marcelo Epstein
      Pages 239-252
  6. Back Matter
    Pages 253-255

About this book

Introduction

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

Keywords

Continuum physics Diffusion equations Non-linear models Discrete vibrating systems Hyperbolic equations Fourier integral Duhamel's principle Green's functions Dirichlet problems

Authors and affiliations

  • Marcelo Epstein
    • 1
  1. 1.Department of Mechanical and Manufacturing EngineeringUniversity of CalgaryCalgaryCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-55212-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-55211-8
  • Online ISBN 978-3-319-55212-5
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site
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