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Mathematical Modelling: A case studies approach
Reinhard Illner, C. Sean Bohun, Samantha McCollum, and Thea van Roode, University of Victoria, BC, Canada

Student Mathematical Library
2005; 196 pp; softcover
Volume: 27
ISBN-10: 0-8218-3650-1
ISBN-13: 978-0-8218-3650-7
List Price: US$41
Institutional Members: US$32.80
All Individuals: US$32.80
Order Code: STML/27
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Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem.

The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel.

Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; others are more modest.

The text was designed to be suitable for a one-term course for advanced undergraduates. The selection of topics and the style of exposition reflect this choice. The authors have also succeeded in demonstrating just how enjoyable the subject can be.

This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.

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Advanced undergraduates, graduate students, and research mathematicians interested in mathematical modelling and applied mathematics.


"IBMvR is a welcome addition to the collection of texts for modeling courses. It fits well [in] its intended audience, all of whom appreciate its small size and reasonable price. I would use it again as the text for my junior/senior-level course, and it should be on anyone's shortlist for such a course."

-- MAA Reviews

"The book is written in a nice manner, the exposition is very friendly and intriguing ... [a] delightful introductory text."

-- Zentralblatt MATH

Table of Contents

  • Crystallization dynamics
  • Will the valve hold?
  • How much will that annuity cost me?
  • Dimensional analysis
  • Predator-prey systems
  • A control problem in fishery management
  • Formal justice
  • Traffic dynamics: A microscopic model
  • Traffic dynamics: Macroscopic modelling
  • Bibliography
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