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  1. differentialequations x
  2. differentialequation x
  3. stability x
  4. ordinarydifferentialequations x
  1. 1-001A-T-MandMDeathImmigration

    27 Jun 2016 | Modeling Scenarios

    Consider a regular size bag of M&M candies (not peanut, just regular). Usually there are about 55 pieces in each bag. They are of different colors, but each piece almost always has an ``m" pressed on one side and not the other. Hence, there are distinctions between the sides. Let us...

  2. 1-001B-T-MAndM-DeathImmigrationMystery

    27 Jun 2016 | Modeling Scenarios

    We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice. Collected data on generation or iteration and population  is then...

  3. 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.

  4. 1-001c-T-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.

  5. 1-001d-T-HotelPopulationDecay

    03 Jul 2019 | Modeling Scenarios

    We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

  6. 1-003-S-Text-IntroNumericalMethods

    10 Jan 2019 | Technique Narratives

    We ask students to develop two numerical methods for solving first order differential equations  geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes. 

  7. 1-003-T-Text-IntroNumericalMethods

    10 Jan 2019 | Technique Narratives

    We develop elementary approaches to numerically solving first order differential equations with Euler's Method and Improved Euler's Method. We ask students to develop these geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different...

  8. 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 ...

  9. 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...

  10. 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...

  11. 1-007-T-AntTunnelBuilding

    31 May 2015 | Modeling Scenarios

    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...

  12. 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.

  13. 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.

  14. 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...

  15. 1-010-Text-T-AtmosphericCO2Bifurcation

    12 Jan 2020 | Technique Narratives

    Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide. carbon dioxide is taken as a parameter and temperature is a function of time. For low values of carbon dioxide, there...

  16. 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...

  17. 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...

  18. 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...

  19. 1-014-T-DrainingContainers

    17 Mar 2017 | Modeling Scenarios

    We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''

  20. 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...