Mathematical Models and Their Analysis

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.

Frederic Y. M. Wan has been a Professor of Mathematics at the University of California, Irvine since 1995, where he was also Chancellor for Research and Dean of Graduate Studies, 1995 2000. He has previously held positions on the mathematics faculty at MIT and as the founding Director of the Institute of Applied Mathematics and Statistics at the University of British Columbia, President of the American Academy of Mechanics (AAM), President of the Canadian Applied Mathematics Society (CAMS/SCMA), and founding Chair of the Department of Applied Mathematics at the Univ