Tags: order

Modeling Scenarios (21-40 of 84)

  1. 10-001-S-TilingHallway

    12 Sep 2019 | | Contributor(s):: Rob Krueger, Eric Stachura

    Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration.  Then students will be introduced to the concept of the shift...

  2. 1-092-S-DashItAll

    01 Sep 2019 | | 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...

  3. 1-001d-S-HotelPopulationDecay

    03 Jul 2019 | | Contributor(s):: Dina Yagodich

    We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

  4. 1-063-S-ThreeHoleColumn

    15 Dec 2018 | | 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.

  5. 1-062-S-BacterialGrowth

    15 Sep 2018 | | 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...

  6. 1-053-S-SlimeSpread

    30 Aug 2018 | | 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.

  7. 7-040-S-TankInterruptMixing

    22 Aug 2018 | | 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.

  8. 7-020-S-ThermometerInVaryingTempStream

    22 Aug 2018 | | 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.

  9. 1-138-S-InnerEarDrugDelivery

    20 Aug 2018 | | 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...

  10. 1-054-S-GrowthInFarmland

    14 Aug 2018 | | 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...

  11. 1-081-S-TumorGrowth

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

    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...

  12. 6-070-S-BeerBubbles

    24 Apr 2018 | | 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...

  13. 1-115-S-ModelingWithFirstOrderODEs

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

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

  14. 1-043-S-CoolingUpAndDown

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

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

  15. 1-057-S-FiguringFluidFlow

    15 Aug 2017 | | 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.

  16. 1-042-S-Kool-Aid

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

    Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...

  17. 1-014-S-DrainingContainers

    17 Mar 2017 | | 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?''

  18. 1-037-S-CommonColdSpread

    30 Nov 2016 | | Contributor(s):: Richard Corban Harwood

    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...

  19. 1-052-S-SaltWaterTanks

    27 Nov 2016 | | Contributor(s):: Brian Winkel

    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

  20. 1-058-S-WaterClocks

    26 Nov 2016 | | Contributor(s):: Sania Qureshi, Brian Winkel

    We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...