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  1. firstorder x
  1. 1-092-T-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  2. 1-092-S-DashItAll

    01 Sep 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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. 1-083-T-FallingMeteorites

    24 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

  4. 1-082-T-MirrorMirror

    21 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

  5. Ice Coverage in the Arctic Climate over time

    17 Aug 2019 | Articles and Publications | Contributor(s): Jessica Libertini

    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...

  6. 1-068-T-WaterBottleCooling

    14 Aug 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    This modeling scenario involves Newton's Law of Cooling and should be appropriate in the first week or even the first day of an introductory differential equations course. The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a...

  7. 1-001d-T-HotelPopulationDecay

    03 Jul 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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.

  8. 1-107-T-ClothDry

    27 Apr 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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...

  9. 5-005-Text-T-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    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...

  10. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    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. 1-125-T-DiceyPopulations

    04 Mar 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...

  12. 1-077-T-RLMSimSeriesCircuit

    03 Mar 2019 | Modeling Scenarios | Contributor(s): Jessica Libertini

    In this validation-oriented setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using Multisim) of the circuit. This is compared...

  13. 1-042-Kool-Aid Modeling Video

    24 Feb 2019 | General Resources | Contributor(s): Jessica Libertini

    This is a video which can be used with students after they have worked on the Modeling Scenario 1-042-KoolAid. Dina Yagodich, Frederick Community College, Frederick MD USA produced the video in support of her students who thoroughly enjoyed doing this Modeling Scenario.This video is only...

  14. 1-003-T-Text-IntroNumericalMethods

    10 Jan 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    We develop elementary approaches to numerically solving first order differential equations with Euler's Method and Improved Euler's Method. We ask students to develop these geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different...

  15. 1-003-S-Text-IntroNumericalMethods

    10 Jan 2019 | Technique Narratives | Contributor(s): Jessica Libertini

    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. 

  16. 1-063-T-ThreeHoleColumn

    15 Dec 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

    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.

  17. 6-024-T-DronePackageDelivery

    18 Sep 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

    In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the...

  18. 1-062-T-BacterialGrowth

    15 Sep 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential growth fit, difference equation, differential equation, and parameter estimation using EXCEL spreadsheet. In this particular modeling...

  19. 6-006-T-ZombieGameHvZ

    09 Sep 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

  20. 1-053-T-SlimeSpread

    30 Aug 2018 | Modeling Scenarios | Contributor(s): Jessica Libertini

    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.