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Modeling Scenarios feed

  1. 1-143-S-PopulationModelVariationsMATLAB

    17 Feb 2019 | Modeling Scenarios | Contributor(s):: Bill Skerbitz

    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations.  They will also work with other utilities...

  2. 3-009-S-BallDropInWater

    16 Dec 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

  3. 1-063-S-ThreeHoleColumn

    15 Dec 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

  4. 3-043-S-BallisticModeling-SpongeDart

    20 Nov 2018 | Modeling Scenarios | Contributor(s):: Jean Marie Linhart, Peter Howard

    The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance. The first two models are based respectively on the common simplifying assumptions of no air resistance and...

  5. 6-065-S-InternetPlatformUsers

    30 Oct 2018 | Modeling Scenarios | Contributor(s):: Victoria Rayskin

    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

  6. 6-011-S - HumansVsZombies

    25 Oct 2018 | Modeling Scenarios | Contributor(s):: Hope McIlwain

    In this activity, students will analyze the SIR differential equations model in the context of a zombie invasion of a human population. First the students will analyze a two equation system representing only two populations, humans and zombies. Then a new population, the recovered zombies, will...

  7. 6-010-S-SocialCampaigns

    23 Sep 2018 | Modeling Scenarios | Contributor(s):: Hyunsun Lee

    Mathematical epidemic models are crucial tools to understand, analyze, predict, and control infectious diseases. The Susceptible-Infected-Recovered (SIR) model is a basic compartment model, describing how an infectious disease propagates through a population. The problem is formulated as a system...

  8. 6-024-S-DronePackageDelivery

    18 Sep 2018 | Modeling Scenarios | Contributor(s):: Eric Stachura, Robert Krueger

    In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the analytical...

  9. 6-019-S-EnablingEpidemicExploration

    17 Sep 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.

  10. 1-062-S-BacterialGrowth

    15 Sep 2018 | Modeling Scenarios | Contributor(s):: Arati Nanda Pati

    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

  11. 6-006-S-ZombieGameHvZ

    09 Sep 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game. Many alternate rule sets provide options to formulate different models. Students solve...

  12. 1-053-S-SlimeSpread

    30 Aug 2018 | Modeling Scenarios | Contributor(s):: Brian Winkel

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

  13. 6-003-S-SchoolFluEpidemic

    28 Aug 2018 | Modeling Scenarios | Contributor(s):: Darrell Weldon Pepper

    We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

  14. 1-141-S-M&MGameRevisited

    27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

    In this project students will learn to find a probability distribution using the classical M&M game in SIMIODE.

  15. 1-108-S-PoissonProcess

    27 Aug 2018 | Modeling Scenarios | Contributor(s):: Mehdi Hakim-Hashemi

    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.

  16. 1-118-S-SolowEconomicGrowth

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Yuri Yatsenko

  17. 7-040-S-TankInterruptMixing

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Norman Loney

    We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

  18. 7-020-S-ThermometerInVaryingTempStream

    22 Aug 2018 | Modeling Scenarios | Contributor(s):: Norman Loney

    We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

  19. 1-138-S-InnerEarDrugDelivery

    20 Aug 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

    Hearing loss is difficult to treat due to the inner ear location and structure. Drawing from this challenging case, this scenario guides students to transform a treatment protocol into a mathematical model. Students engage in pre-clinical studies to examine local drug delivery to the cochlea. The...

  20. 4-055-S-ShatterWineGlass

    20 Aug 2018 | Modeling Scenarios | Contributor(s):: Jue Wang

    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important? Three cases are presented: shattering a wine glass, collapse of a suspension bridge, and crash of...