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  1. differentialequations x
  1. 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.

  2. 1-024-T-MalariaControl

    06 May 2016 | Modeling Scenarios

    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...

  3. 1-028-T-SouthernSweetIcedTea

    25 Jun 2016 | Modeling Scenarios

    We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea.  We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.

  4. 1-032-S-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios

    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

  5. 1-032-T-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios

    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

  6. 1-034-T-FishMixing

    24 Dec 2015 | Modeling Scenarios

    This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking and fishing plan in a lake.  The mixture is of two species of fish, one being the current sole...

  7. 1-044-T-CollegeBound

    31 Jul 2016 | Modeling Scenarios

    Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.

  8. 1-050-T-BargingAhead

    10 Feb 2016 | Modeling Scenarios

    As captain of a barge, you need to determine how fast to transport your 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,...

  9. 1-061-T-PotatoCooling

    05 Oct 2016 | Modeling Scenarios

    We model the cooling of a baked potato and compare it to student-collected data.

  10. 1-064-T-TorricelliBox

    14 Aug 2017 | Modeling Scenarios

    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.

  11. 1-065-T-Algal Blooms

    26 Jul 2016 | Modeling Scenarios

    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994. After reading a summary of articles written on the incidents, students are guided through the process of creating a first order differential equation from a verbal model of the...

  12. 1-066-S-USCensusModeling

    15 Sep 2017 | Modeling Scenarios

    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled.

  13. 1-066-T-USCensusModeling

    15 Sep 2017 | Modeling Scenarios

    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions. Analysis of the per-unit population growth leads to an understanding of the assumptions underlying each model. Parameters in...

  14. 1-081-S-TumorGrowth

    09 Jun 2018 | Modeling Scenarios

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  15. 1-081-T-TumorGrowth

    09 Jun 2018 | Modeling Scenarios

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  16. 1-095-T-RatingChessPlayers

    17 Aug 2016 | Modeling Scenarios

    The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario. In the first part of the activity, students will read a description of a method used to rate chess players. From the verbal...

  17. 1-108-S-PoissonProcess

    27 Aug 2018 | Modeling Scenarios

    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

  18. 1-108-T-PoissonProcess

    27 Aug 2018 | Modeling Scenarios

    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

  19. 1-115-S-ModelingWithFirstOrderODEs

    04 Sep 2017 | Modeling Scenarios

    Several models using first order differential equations are offered with some questions on formulating a differential equations model

  20. 1-115-T-ModelingWithFirstOrderODEs

    04 Sep 2017 | Modeling Scenarios

    Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.