
1143SPopulationModelVariationsMATLAB
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...

3009SBallDropInWater
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.

1063SThreeHoleColumn
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.

3043SBallisticModelingSpongeDart
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...

6065SInternetPlatformUsers
30 Oct 2018  Modeling Scenarios  Contributor(s):: Victoria Rayskin
A model estimating the volume of users interacting through a twosided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

6011S  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...

6010SSocialCampaigns
23 Sep 2018  Modeling Scenarios  Contributor(s):: Hyunsun Lee
Mathematical epidemic models are crucial tools to understand, analyze, predict, and control infectious diseases. The SusceptibleInfectedRecovered (SIR) model is a basic compartment model, describing how an infectious disease propagates through a population. The problem is formulated as a system...

6024SDronePackageDelivery
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...

6019SEnablingEpidemicExploration
17 Sep 2018  Modeling Scenarios  Contributor(s):: Brian Winkel
We offer several strategies for estimating parameters in models of epidemics, one using a MichaelisMenten saturation infected rate.

1062SBacterialGrowth
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...

6006SZombieGameHvZ
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 nonlinear differential equations to model the HvZ game. Many alternate rule sets provide options to formulate different models. Students solve...

1053SSlimeSpread
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.

6003SSchoolFluEpidemic
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.

1141SM&MGameRevisited
27 Aug 2018  Modeling Scenarios  Contributor(s):: Mehdi HakimHashemi
In this project students will learn to find a probability distribution using the classical M&M game in SIMIODE.

1108SPoissonProcess
27 Aug 2018  Modeling Scenarios  Contributor(s):: Mehdi HakimHashemi
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.

1118SSolowEconomicGrowth
22 Aug 2018  Modeling Scenarios  Contributor(s):: Yuri Yatsenko

7040STankInterruptMixing
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.

7020SThermometerInVaryingTempStream
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.

1138SInnerEarDrugDelivery
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 preclinical studies to examine local drug delivery to the cochlea. The...

4055SShatterWineGlass
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...