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Modeling Scenarios feed

  1. 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.

  2. 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...

  3. 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...

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 1-064-S-TorricelliBox

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

    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.

  10. 3-075-S-RLCCircuit

    17 May 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

  11. 5-080-S-SpaceFlightRecolonize

    06 May 2017 | Modeling Scenarios | Contributor(s):: Brian Allen, Karoline Hood

    This project is a combination of differential equations, multi-variable calculus, and vector calculus with the use of technology to model colonization of a new planet.

  12. 1-042-S-Kool-Aid

    26 Apr 2017 | Modeling Scenarios | Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon

    We model the amount of drink powder in a second tank of a two tank flow system.

  13. 1-074-S-BottleWaterFlow

    17 Apr 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow from a container.

  14. 1-073-S-WaterExitBottle

    17 Apr 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.

  15. 6-023-S-DroneHeadingHome

    13 Apr 2017 | Modeling Scenarios | Contributor(s):: Richard Spindler

    You just received a new long-range helicopter drone for your birthday! After a little practice, you try a long-range test of it by having it carry a small package to your home. A friend volunteers to take it 5 miles east of your home with the goal of flying directly back to your home. So you...

  16. 3-040-S-FirstPassageTime

    07 Apr 2017 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time with several applications.

  17. 3-002-S-ModelsMotivatingSecondOrder

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

    We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...

  18. 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.

  19. 3-004-S-VanderPol

    21 Mar 2017 | Modeling Scenarios | Contributor(s):: Mark A. Lau Kwan

    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation. The spreadsheet features a number of dynamic controls that permit the user to alter the parameters of the Van der Pol equation and explore the...

  20. 1-014-S-DrainingContainers

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

    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?''