Tags: Guide

Modeling Scenarios (1-15 of 15)

  1. 1-002-S-Tossing

    11 May 2015 | | Contributor(s):: Brian Winkel

    We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.We add a Hand Out Working Version which can be used in class authored by Rachel ...

  2. 1-007-S-AntTunnelBuilding

    31 May 2015 | | Contributor(s):: Brian Winkel

    We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION  We have placed in Supporting Docs both...

  3. 1-009-S-ICUSpread

    02 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

  4. 1-012-S-SublimationCarbonDioxide

    03 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer data on the sublimation of dry ice (carbon dioxide) with data collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the differential equation, estimate the parameters in...

  5. 1-018-S-LogisticPopGrowth

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic  model in these situations. 

  6. 1-025-S-MixingItUp

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

  7. 1-026-S-Evaporation

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We  ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...

  8. 1-036-S-NeutralBuoyancy

    03 Jun 2016 | | Contributor(s):: John Thomas Sieben

    Things float or they don’t.  Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...

  9. 1-039-S-StochasticPopModels

    11 Sep 2016 | | Contributor(s):: Dan Flath

    We offer students the opportunity to develop several strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t. We go further...

  10. 1-050-S-BargingAhead

    10 Feb 2016 | | Contributor(s):: Timothy Pennings

    As captain of a barge, you need to determine how fast to transportyour barge up river against the current in order to minimize the expended energy.Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if...

  11. 1-052-S-SaltWaterTanks

    27 Nov 2016 | | Contributor(s):: Brian Winkel

    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

  12. 1-054-S-GrowthInFarmland

    14 Aug 2018 | | Contributor(s):: Richard Spindler

    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

  13. 1-058-S-WaterClocks

    26 Nov 2016 | | Contributor(s):: Sania Qureshi, Brian Winkel

    We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...

  14. 1-062-S-BacterialGrowth

    15 Sep 2018 | | Contributor(s):: Arati Nanda Pati

    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

  15. 7-008-S-MachineReplacement

    04 Jun 2015 | | Contributor(s):: Brian Winkel

      Students build an differential equation model using a convolution for machine replacement strategies for two different machine failure models: (1) exponentially distributed failure (student exercise) and (2) fixed time replacement. We discuss all the necessary probability notions which...