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  1. 1-090-S-EmptySphericalTank

    12 Nov 2016 | Modeling Scenarios | Contributor(s): Brian Winkel

  2. 1-091-S-Slopefields

    04 Sep 2017 | Modeling Scenarios | Contributor(s): Ben Dill, Holly Zullo

    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves. In this activity, students are introduced to the concepts of...

  3. 1-092-S-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s): Kurt Bryan

    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a...

  4. 1-093-S-SucroseReaction

    19 Jul 2016 | Modeling Scenarios | Contributor(s): Brian Winkel

  5. 1-094-S-SteepingTea

    12 Sep 2017 | Modeling Scenarios | Contributor(s): Eric Sullivan, Jesica Bauer, Erica Wiens

    In this activity, we provide photographs of the steeping process for a fruit tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration of the tea oils in...

  6. 1-095-S-RatingChessPlayers

    17 Aug 2016 | Modeling Scenarios | Contributor(s): Hope McIlwain

  7. 1-101-S-ClassM&MDeathAndImmigration

    07 Nov 2015 | Modeling Scenarios | Contributor(s): Brian Winkel

  8. 1-102-S-CancerGrowth

    29 Jul 2018 | Modeling Scenarios | Contributor(s): Jue Wang

    This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...

  9. 1-105-S-AnimalFall

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

    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

  10. 1-107-S-ClothDry

    27 Apr 2019 | Modeling Scenarios | Contributor(s): Brian Winkel

    We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...

  11. 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.

  12. 1-109-S-EmployeeAttrition

    25 Mar 2019 | Modeling Scenarios | Contributor(s): Lyle Clifford Smith

    This scenario models the loss of employees and the employer's attempt to retain them through stock options. This is intended for introductory students and is paired well with exponential growth/decay material. We also introduce the 5% rule to sort possible factors into assumptions and...

  13. 1-110-S-SnailsInaTidePool

    04 Oct 2016 | Modeling Scenarios | Contributor(s): Lisa Driskell, Audrey Malagon

  14. 1-111-S-SpreadOfInformation

    02 Sep 2019 | Modeling Scenarios | Contributor(s): Jeff Pettit

    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...

  15. 1-114-S-EarthClimate

    09 Dec 2019 | Modeling Scenarios | Contributor(s): Terrance Pendleton

    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth from solar radiation, emission of radiation to outer space, and Earth's...

  16. 1-115-S-ModelingWithFirstOrderODEs

    04 Sep 2017 | Modeling Scenarios | Contributor(s): Michael Grayling

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

  17. 1-116-S-TropicalStormWindspeeds

    12 Jan 2020 | Modeling Scenarios | Contributor(s): Terrance Pendleton

    We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential equation model.

  18. 1-118-S-SolowEconomicGrowth

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

  19. 1-120-S-CircularRollerCoaster

    27 Sep 2016 | Modeling Scenarios | Contributor(s): Kevin S Huang

  20. 1-122-S-SpreadPEV

    28 Mar 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    We present data on world sales data of plug-in electric vehicles (PEVs) and request a model on the rate of change in sales over time, leading to predection as to number of PEVs in the future.