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Methods of Mathematical Modelling

Continuous Systems and Differential Equations

  • Thomas Witelski
  • Mark Bowen

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

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Formulation of Models

    1. Front Matter
      Pages 1-1
    2. Thomas Witelski, Mark Bowen
      Pages 3-21
    3. Thomas Witelski, Mark Bowen
      Pages 23-45
    4. Thomas Witelski, Mark Bowen
      Pages 47-83
    5. Thomas Witelski, Mark Bowen
      Pages 85-110
  3. Solution Techniques

    1. Front Matter
      Pages 111-111
    2. Thomas Witelski, Mark Bowen
      Pages 113-125
    3. Thomas Witelski, Mark Bowen
      Pages 127-145
    4. Thomas Witelski, Mark Bowen
      Pages 147-165
    5. Thomas Witelski, Mark Bowen
      Pages 167-183
    6. Thomas Witelski, Mark Bowen
      Pages 185-200
    7. Thomas Witelski, Mark Bowen
      Pages 201-213
    8. Thomas Witelski, Mark Bowen
      Pages 215-232
  4. Case Studies

    1. Front Matter
      Pages 233-233
    2. Thomas Witelski, Mark Bowen
      Pages 235-249
  5. Back Matter
    Pages 251-305

About this book

Introduction

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics.

Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems.

Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Keywords

Asymptotic Analysis Calculus of Variations Mathematical Modelling Multiple Scale Analysis Nonlinear Oscillators Ordinary Differential Equations Partial Differential Equations Perturbation Methods

Authors and affiliations

  • Thomas Witelski
    • 1
  • Mark Bowen
    • 2
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.International Center for Science and Engineering ProgramsWaseda UniversityTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-23042-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-23041-2
  • Online ISBN 978-3-319-23042-9
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site
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