**Student Mathematical Library**

Volume: 27;
2005;
196 pp;
Softcover

MSC: Primary 00;
Secondary 93

**Print ISBN: 978-0-8218-3650-7
Product Code: STML/27**

List Price: $44.00

Individual Price: $35.20

**Electronic ISBN: 978-1-4704-1215-9
Product Code: STML/27.E**

List Price: $41.00

Individual Price: $32.80

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#### Supplemental Materials

# Mathematical Modelling: A case studies approach

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*Reinhard Illner; C. Sean Bohun; Samantha McCollum; Thea van Roode*

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.

#### Readership

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

#### Reviews & Endorsements

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

# Table of Contents

## Mathematical Modelling: A case studies approach

- Cover Cover11
- Title i2
- Copyright i2
- Contents vii8
- Preface xi12
- Chapter 1. Crystallization Dynamics 118
- §1.1. Derivation of the K-A Model 320
- §1.2. Emergence of the Poisson Distribution from the Binomial Distribution 623
- §1.3. Testing the K-A Model 724
- §1.4. A New Model 825
- §1.5. The Averaging Process 1128
- §1.6. Choosing the Probability Density f 1128
- §1.7. Why Did the K-A Model Fail? 1532
- Exercises 1532
- Notes 2037

- Chapter 2. Will the Valve Hold? 2138
- §2.1. Terminology 2340
- §2.2. The Relevant Forces 2441
- §2.3. The Equation of Motion 2643
- §2.4. Analysis: Is the Initial Value Problem Well-Posed? 2744
- §2.5. Revising the Model 2845
- §2.6. Revision 1: Adding a Reference Distance 3148
- §2.7. Revision 2: Changing the Initial Conditions 3249
- §2.8. P[sub(max)]: The Maximal Pressure 3451
- Exercises 3754
- Notes 3956

- Chapter 3. How Much Will that Annuity Cost Me? 4158
- Chapter 4. Dimensional Analysis 6380
- Chapter 5. Predator-Prey Systems 83100
- §5.1. The Lotka–Volterra Model 83100
- §5.2. The Effect of Interference on the System 87104
- §5.3. Linearization: The General Procedure 92109
- §5.4. Solving Linear Systems 95112
- §5.5. Classification of the Equilibria 98115
- §5.6. The Phase Paths 101118
- §5.7. Multiple Species 104121
- §5.8. Exploration A: Structural Stability 105122
- §5.9. Exploration B: The Lorenz Attractor 110127
- Exercises 114131

- Chapter 6. A Control Problem in Fishery Management 119136
- Chapter 7. Formal Justice 131148
- Chapter 8. Traffic Dynamics: A Microscopic Model 149166
- Chapter 9. Traffic Dynamics: Macroscopic Modelling 169186
- Bibliography 195212
- Back Cover Back Cover1216