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  1. mathematica x
  2. differentialequations x
  1. 1-001-T-MandMDeathAndImmigration

    30 May 2015 | Modeling Scenarios

    We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their...

  2. 1-001c-S-PopulationDecayThenSome

    18 Jun 2019 | Modeling Scenarios

    This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

  3. 1-002-T-Tossing

    11 May 2015 | Modeling Scenarios

    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 ...

  4. 1-003-T-CollegeSavings

    12 May 2015 | Modeling Scenarios

    We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.

  5. 1-004-T-MicroorganismImmigration

    30 May 2015 | Modeling Scenarios

    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

  6. 1-005-T-OilSlick

    30 May 2015 | Modeling Scenarios

    We describe a modeling activity for students in  which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...

  7. 1-005A-T-ChemDataCollection

    30 May 2015 | Modeling Scenarios

    We present a situation in which a chemistry graduate student is assigned the  task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of...

  8. 1-005B-T-ChemDataCollection

    30 May 2015 | Modeling Scenarios

    We present a situation in which a chemistry graduate student is assigned the  task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...

  9. 1-006-T-FinancingSavingsAndLoans

    31 May 2015 | Modeling Scenarios

    We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose.  In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...

  10. 1-009-T-ICUSpread

    02 Jun 2015 | Modeling Scenarios

    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.

  11. 1-009-T-Text-Bifurcation

    31 May 2015 | Technique Narratives

    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.

  12. 1-010-T-LSDAndProblemSolving

    02 Jun 2015 | Modeling Scenarios

    We describe the use of  a two compartment model of a linear system of first order linear differential equations to model  lysergic acid diethylamide (LSD) in the body. We provide the data from the literature. We offer students the opportunity to build a two compartment model to fully...

  13. 1-011-T-Kinetics

    03 Jun 2015 | Modeling Scenarios

    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions and offer many opportunities to model these...

  14. 1-012-T-SublimationCarbonDioxide

    03 Jun 2015 | Modeling Scenarios

    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...

  15. 1-013-T-Sleuthing

    03 Jun 2015 | Modeling Scenarios

    We present several situations in which differential equation models serve to aid in sleuthing and general investigations. One involves initial speed given information about constant deceleration and distance to stop in traffic incident; one involves modeling a steel ball launched vertically and...

  16. 1-015-T-Torricelli

    03 Jun 2015 | Modeling Scenarios

    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We offer several sources of simulations on YouTube and at this site from which we collect data and ask students to verify...

  17. 1-017-T-DiseaseSpread

    04 Jun 2015 | Modeling Scenarios

    We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways)  in a differential equation model for the spread of the disease. Students ...

  18. 1-017a-T-DiseaseSpread

    04 Jun 2015 | Modeling Scenarios

    We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways)  in a differential equation model for the spread of the disease. Students ...

  19. 1-018-T-LogisticPopGrowth

    04 Jun 2015 | Modeling Scenarios

     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. 

  20. 1-019-T-RocksInTheHead

    04 Jun 2015 | Modeling Scenarios

     We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...