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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

101 total view(s), 27 download(s)

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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Article Context

Resource Type
Qualitative Analysis
Technology
Approach
Skills
Assessment Type
Pedagogical Approaches
Bloom's Cognitive Level

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.

Article Files

Authors

Author(s): William (Bill) Skerbitz

Wayzata High School, Plymouth MN USA

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