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Compartmental Modeling with Networks

  • Gilbert G. Walter
  • Martha Contreras

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Introduction and Simple Examples

    1. Gilbert G. Walter, Martha Contreras
      Pages 1-8
  3. Structure of Models: Directed Graphs

    1. Front Matter
      Pages 9-9
    2. Gilbert G. Walter, Martha Contreras
      Pages 11-16
    3. Gilbert G. Walter, Martha Contreras
      Pages 17-24
    4. Gilbert G. Walter, Martha Contreras
      Pages 25-40
    5. Gilbert G. Walter, Martha Contreras
      Pages 41-46
    6. Gilbert G. Walter, Martha Contreras
      Pages 47-51
    7. Gilbert G. Walter, Martha Contreras
      Pages 53-61
  4. Digraphs and Probabilities: Markov Chains

    1. Front Matter
      Pages 63-63
    2. Gilbert G. Walter, Martha Contreras
      Pages 65-69
    3. Gilbert G. Walter, Martha Contreras
      Pages 71-80
    4. Gilbert G. Walter, Martha Contreras
      Pages 81-87
    5. Gilbert G. Walter, Martha Contreras
      Pages 89-99
    6. Gilbert G. Walter, Martha Contreras
      Pages 101-108
  5. Compartmental Models: Applications

    1. Front Matter
      Pages 109-109
    2. Gilbert G. Walter, Martha Contreras
      Pages 111-123
    3. Gilbert G. Walter, Martha Contreras
      Pages 125-129
    4. Gilbert G. Walter, Martha Contreras
      Pages 131-139
    5. Gilbert G. Walter, Martha Contreras
      Pages 141-148
    6. Gilbert G. Walter, Martha Contreras
      Pages 149-162
    7. Gilbert G. Walter, Martha Contreras
      Pages 163-171
  6. Compartmental Models Theory

    1. Front Matter
      Pages 173-173
    2. Gilbert G. Walter, Martha Contreras
      Pages 175-182
    3. Gilbert G. Walter, Martha Contreras
      Pages 183-196
    4. Gilbert G. Walter, Martha Contreras
      Pages 197-210
    5. Gilbert G. Walter, Martha Contreras
      Pages 211-217
    6. Gilbert G. Walter, Martha Contreras
      Pages 218-227
  7. Back Matter
    Pages 228-250

About this book

Introduction

The subject of mathematical modeling has expanded considerably in the past twenty years. This is in part due to the appearance of the text by Kemeny and Snell, "Mathematical Models in the Social Sciences," as well as the one by Maki and Thompson, "Mathematical Models and Applica­ tions. " Courses in the subject became a widespread if not standard part of the undergraduate mathematics curriculum. These courses included var­ ious mathematical topics such as Markov chains, differential equations, linear programming, optimization, and probability. However, if our own experience is any guide, they failed to teach mathematical modeling; that is, few students who completed the course were able to carry out the mod­ eling paradigm in all but the simplest cases. They could be taught to solve differential equations or find the equilibrium distribution of a regular Markov chain, but could not, in general, make the transition from "real world" statements to their mathematical formulation. The reason is that this process is very difficult, much more difficult than doing the mathemat­ ical analysis. After all, that is exactly what engineers spend a great deal of time learning to do. But they concentrate on very specific problems and rely on previous formulations of similar problems. It is unreasonable to expect students to learn to convert a large variety of real-world problems to mathematical statements, but this is what these courses require.

Keywords

Applied math Maple Markov mathematical modeling model modeling

Authors and affiliations

  • Gilbert G. Walter
    • 1
  • Martha Contreras
    • 2
  1. 1.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA
  2. 2.Department of BiometryCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1590-5
  • Copyright Information Birkhäuser Boston 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7207-6
  • Online ISBN 978-1-4612-1590-5
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site
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