Mathematical Modeling

  • Glenn Ledder
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


Mathematical modeling refers to any use of mathematics to do theoretical science. As such, it incorporates mathematical techniques into a larger structure that is seldom taught in mathematics courses. Models can be derived from mechanistic principles or based on empirical data; there are some commonalities between these types of modeling as well as important differences. The first two sections present the concepts of mathematical modeling. Three sections on empirical modeling develop the least squares method for fitting linear models, extend the method for use with a large class of nonlinear models, and present the Akaike information criterion (AIC) for model selection. Two sections on mechanistic modeling present basic methods for model derivation and nondimensionalization. Biological examples in this chapter include a discussion of the use and misuse of the Lotka–Volterra predator–prey model, the derivation of the Holling type II predation model, and a compartment model of pollution in a lake. The problems include several that use chemostat and SIR disease models and an exploration of the evidence for global warming provided by an extensive data set of grape harvest dates.


Conceptual Model Akaike Information Criterion Virtual World Prey Animal Holling Type 
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Glenn Ledder
    • 1
  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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