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  1. differentialequations x
  2. differentialequation x
  1. 1-001B-S-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...

  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. 1-001d-S-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.

  4. 1-003-S-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. 1-003-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. 

  6. 1-004-S-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.

  7. 1-005-S-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 ...

  8. 1-005A-S-OilSlick

    30 May 2015 | Modeling Scenarios

  9. 1-014-S-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?''

  10. 1-021-S-FeralCatControl

    24 Jan 2016 | Modeling Scenarios

    This activity is structured as a letter from a company seeking assistance with a mathematical problem. The students will act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use...

  11. 1-022-S-SpreadOfTechnology

    27 Nov 2015 | Modeling Scenarios

    We examine  plots on the  spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

  12. 1-024-S-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...

  13. 1-027-S-StochasticProcesses

    04 Jun 2015 | Modeling Scenarios

    We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...

  14. 1-028-S-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.

  15. 1-029-S-ConeToCubeFlow

    02 Mar 2016 | Modeling Scenarios

    We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom  is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

  16. 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...

  17. 1-032-S-WordPropagation

    07 Apr 2016 | Modeling Scenarios

    This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.

  18. 1-034-S-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...

  19. 1-036-S-NeutralBuoyancy

    03 Jun 2016 | Modeling Scenarios

    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...

  20. 1-037-S-CommonColdSpread

    30 Nov 2016 | Modeling Scenarios

    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...

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