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# Mathematical Models and Their Analysis

### by Frederic Y. M. Wan

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2018 / xx + 402 pages / softcover / ISBN 978-1-611975-26-0 / List Price $74.00 / SIAM Member Price$51.80 / Order Code: CL79

Keywords: applied mathematics, mathematical modeling

Contents
Preface to the Classics Edition;
Preface;
Chapter 1: Groping in the Dark: Introduction;

Part I: Evolution of Dynamical Systems;
Chapter 2: Here Comes the Sun: The Three Laws of Kepler;
Chapter 3: Slower Than Light: The Precession of the Perihelion of the Planet Mercury;

Part II: Stability of Equilibrium Configuration;
Chapter 4: Swing Low: The Stability of Periodic Orbits;
Chapter 5: Hair: Euler Buckling and Elastic Stability;
Chapter 6: A Menace on Any Road: Car Following;

Part III: Wave Propagation;
Chapter 7: The Shock of the Crash: Traffic Flow on a Long and Crowded Road;
Chapter 8: It’s a Bore: Shallow Water Waves;
Chapter 9: The Sound of Music: Vibrating Strings and Membranes;

Part IV: Diffusion;
Chapter 10: A Hot Rod in Traffic: Sensitivity to a Sharp Traffic Density Gradient;
Chapter 11: Fishing is Strictly prohibited: The 200-Mile Fishing Limit;

Part V: Control and Optimization;
Chapter 12: Suburbs are for the Affluent: The Structure of the Residential District;
Chapter 13: Pay or Save: neoclassical Economic Growth Theory;
Chapter 14: Justice for All: Exhaustible Resources and Intergenerational Equity;
Chapter 15: Timberrr: Economically Optimal Forest Harvesting Schedule;

Appendix to the Classics Edition;
Bibliography;
Index.

A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way.

The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time.

The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.

Audience
This book is recommended for advanced undergraduates, early graduate students, or anyone with a strong background in calculus and ordinary differential equations, for use in mathematical modeling and introduction to applied mathematics courses.