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  1. 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. 1-003-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.

  3. 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. 

  4. 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?''

  5. 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...

  6. 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.

  7. 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...

  8. 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...

  9. 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.

  10. 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...

  11. 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...

  12. 1-039-S-StochasticPopModels

    11 Sep 2016 | Modeling Scenarios

    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...

  13. 1-042-S-Kool-Aid

    26 Apr 2017 | Modeling Scenarios

    Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...

  14. 1-043-S-CoolingUpAndDown

    26 Aug 2017 | Modeling Scenarios

    We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

  15. 1-051-S-OneTankSaltModel

    23 Jul 2016 | Modeling Scenarios

    We offer students a chance to model a one compartment salt mixing model.

  16. 1-053-S-SlimeSpread

    30 Aug 2018 | Modeling Scenarios

    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

  17. 1-055-S-WaterFallingInCone

    27 Feb 2016 | Modeling Scenarios

    There are three videos associated with this Modeling Scenario and all are available on SIMIODE YouTube Channel: Capture-3 YouTube Version SlowMoCapture-1 YouTube Version SlowMoCapture-2 YouTubeVersion and as streaming videos or down loads in this Modeling Scenario under the Supporting Docs Tab...

  18. 1-057-S-FiguringFluidFlow

    15 Aug 2017 | Modeling Scenarios

    We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

  19. 1-058-S-WaterClocks

    26 Nov 2016 | Modeling Scenarios

    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...

  20. 1-059-S-ContainerShapeFallingWater

    22 Nov 2016 | Modeling Scenarios

    We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.

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