A Concrete Approach to Mathematical Modelling / Edition 1

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An engrossing, how-to book designed to pique students' interest in the process of modelling in order to acquire both critical and creative modelling skills and the confidence to apply them. The author uses exercises, case studies and models, based on scientific literature, that are freely adaptable and presented in a fresh perspective as interlocking fragments of a mosaic. Examples are chosen from population dynamics, heat flow, optimal harvesting, traffic management and other areas that use models. Includes material for model builders.
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Editorial Reviews

A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780471109600
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 4/28/1995
  • Edition description: REV
  • Edition number: 1
  • Pages: 624
  • Product dimensions: 6.32 (w) x 9.44 (h) x 1.33 (d)

Meet the Author

Mike Mesterton-Gibbons, PhD, is Professor of Mathematics at Florida State University.

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Table of Contents

An ABC of modelling
I The Deterministic View
1 Growth and decay. Dynamical systems 3
2 Equilibrium 46
3 Optimal control and utility 91
II Validating a Model
4 Validation: accept, improve, or reject 127
III The Probabilistic View
5 Birth and death. Probabilistic dynamics 175
6 Stationary distributions 208
7 Optimal decision and reward 237
IV The Art of Application
8 Using a model: choice and estimation 275
9 Building a model: adapting, extending, and combining 327
V Toward More Advanced Models
10 Further dynamical systems 383
11 Further flow and diffusion 416
12 Further optimization 458
Epilogue 514
Appendix 1: A review of probability and statistics 516
Appendix 2: Models, sources, and further reading arranged by discipline 531
Solutions to selected exercises 539
References 583
Index 591
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