A first course in mathematical modeling
This text provides an introduction to the entire modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem solving process to enhance a student's problem solving capabilities. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible, beginning with short projects, the book facilitates their progressive development and confidence in mathematics and modeling.
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CREATIVE MODEL CONSTRUCTION AND THE MODELING PROCESS
The Modeling Process
Modeling Using Proportionality
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absolute deviation algorithm amount analyze approximate arms race arrival assume assumptions baleen whales behavior braking distance Calculate Chapter consider constant construct Country cubic spline data points delivery density depicted in Figure derivative determine differential equations dimension dimensional analysis dimensionless products discussed divided difference drag force elevator empirical model equilibrium estimate example factors fish function gasoline geometrically similar given graph graphical model growth increase initial integer interval inventory krill least-squares criterion length linear program linear spline mathematical model maximum minimize modeling process Monte Carlo simulation obtain optimal phase plane plot polynomial population level predict probabilistic problem proportional proportionality quadratic quantity queue random number represents rest point scatterplot Section Ship situation slope solve speed Step stopping distance storage cost submodel Suppose Table take-up reel tion total number trajectory UMAP unloading values variables various velocity versus waiting weight whale X force yields zero