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Modeling Scenario

1-190-IntroClass-ModelingScenario

Author(s): William (Bill) Skerbitz

Wayzata High School, Plymouth MN USA

Keywords: population dynamics predator-prey logistic exponential graphical interpretations qualitative analysis

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Abstract

Resource Image Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.

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Description

Furthermore, students will be reminded or introduced to key ideas such as particular and general solutions, interpretation of derivatives, qualitative analysis, graphical interpretation of P vs. t graphs as well as dP/dt vs. P graphs, phase lines, and phase planes. We use this activity on the first day of class, and its overall purpose is to:

  1. Get students introducing, talking, and working with one another.
  2. Set the tone for the level of qualitative analysis expected of students - no question is ``too basic" in their analysis of a situation and the mathematical translation thereof.
  3. Review ideas from Calculus (which they may not have seen for a year or more).
  4. Get students to shift their thinking to emph{start} with considering the rate of change instead of starting with a given function and differentiating it.
  5. Introduce students to the utility of differential equations.
  6. Introduce students to a few of the many tools that will be used throughout the course.

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Authors

Author(s): William (Bill) Skerbitz

Wayzata High School, Plymouth MN USA

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