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Modeling Scenarios feed

  1. 1-089-S-SpreadOfDisease

    15 Aug 2018 | Modeling Scenarios | Contributor(s):: Shinemin Lin

    In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

  2. 1-054-S-GrowthInFarmland

    14 Aug 2018 | Modeling Scenarios | Contributor(s):: Richard Spindler

    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

  3. 6-007-S-FunctionsAndDerivativesInSIRModels

    12 Aug 2018 | Modeling Scenarios | Contributor(s):: Meredith Greer

  4. 5-026-S-Evictions

    12 Aug 2018 | Modeling Scenarios | Contributor(s):: Mary Vanderschoot

  5. 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...

  6. 1-081-S-TumorGrowth

    09 Jun 2018 | Modeling Scenarios | Contributor(s):: Ryan Miller, Randy Boucher

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  7. 6-018-S-ExploringSIRModel

    30 May 2018 | Modeling Scenarios | Contributor(s):: Stanley Florkowski, Ryan Miller

    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting...

  8. 6-026-S-IsleRoyaleModeling

    20 May 2018 | Modeling Scenarios | Contributor(s):: Steven Morse, Brian Allen, Stanley Florkowski

    The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle. This setting allows us to also employ multivariable optimization as a means of model fitting and multivariable integration in the context of...

  9. 6-070-S-BeerBubbles

    24 Apr 2018 | Modeling Scenarios | Contributor(s):: Michael Karls

    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.  The system solution is then used to verify...

  10. 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.

  11. 3-095-S-ShotInWater

    05 Apr 2018 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene: Do bullets moving through water slow as dramatically as depicted in the movies, so that someone a few...

  12. 1-079-S-HomeHeating

    30 Jan 2018 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project concerns the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return? Both scenarios are analyzed in a series of exercises.

  13. 1-066-S-USCensusModeling

    15 Sep 2017 | Modeling Scenarios | Contributor(s):: Jean Marie Linhart

    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled.

  14. 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...

  15. 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...

  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. 1-086-S-MedicinalPill

    31 Aug 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    Administration of a medicinal pill in single and multiple doses is modeled.

  18. 1-071-S-NewtonWatsonTimeOfDeath

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

    Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis.

  19. 1-043-S-CoolingUpAndDown

    26 Aug 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

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

  20. 1-057-S-FiguringFluidFlow

    15 Aug 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    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.