Tags: first order

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  1. 1-088-S-RoomTemperature

    15 Jun 2020 | | Contributor(s):: Tracy Weyand

    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

  2. 1-136-S-MarriageAge

    11 Jun 2020 | | Contributor(s):: Tracy Weyand

    Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...

  3. 1-128-S-RocketFlight

    04 Jun 2020 | | Contributor(s):: Brian Winkel

    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

  4. 1-124-S-WorldPopulation

    30 May 2020 | | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel

    We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION  We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be x-y-S-Title-StudentVersion-Czech.

  5. Transient and Steady State response in RC or RL circuits

    16 Apr 2020 | | Contributor(s):: Brian Winkel

    Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides, This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

  6. 1999-McCartneyCarey-ModelingTrafficFlow

    05 Apr 2020 | | Contributor(s):: Brian Winkel

    1999-McCartneyCarey-ModelingTrafficFlowMcCartney, Mark  and Malachy Carey. 1999. Modelling Traffic Flow: Solving and Interpreting Differential Equations.  Teaching Mathematics and its Applications: An International Journal of the IMA. 18(3):...

  7. 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...

  8. Ice Coverage in the Arctic Climate over time

    17 Aug 2019 | | Contributor(s):: Wisam Victor Yossif Bukaita, Kelcey Meaney, Angie Dimopulos

    In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...

  9. 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.

  10. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | | Contributor(s):: Kurt Bryan

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  11. 1-003-S-Text-IntroNumericalMethods

    10 Jan 2019 | | Contributor(s):: Brian Winkel

    We ask students to develop two numerical methods for solving first order differential equations  geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes. 

  12. 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.

  13. 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...

  14. 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.

  15. 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.

  16. 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.

  17. 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...

  18. 2-001-Text-S-NumericalMethodsComparisons

    18 Aug 2018 | | Contributor(s):: Swarn Singh

    It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

  19. 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...

  20. 1-081-S-TumorGrowth

    09 Jun 2018 | | 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...

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