
1088SRoomTemperature
15 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
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...

1136SMarriageAge
11 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
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 firstorder ordinary differential equations (which...

1128SRocketFlight
04 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
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.

1124SWorldPopulation
30 May 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
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 xySTitleStudentVersionCzech.

Transient and Steady State response in RC or RL circuits
16 Apr 2020  Presentations  Contributor(s): Jessica Libertini
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...

1999McCartneyCareyModelingTrafficFlow
05 Apr 2020  Potential Scenario Ideas  Contributor(s): Jessica Libertini
1999McCartneyCareyModelingTrafficFlowMcCartney, 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):...

1092SDashItAll
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 HillKeller model for a...

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...

1001dSHotelPopulationDecay
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.

5005TextSStiffDifferentialEquations
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...

1003STextIntroNumericalMethods
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.

1053SSlimeSpread
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.

7040STankInterruptMixing
22 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
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.

7020SThermometerInVaryingTempStream
22 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
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.

1138SInnerEarDrugDelivery
20 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
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 preclinical studies to examine local drug delivery to the cochlea. The...

2001TextSNumericalMethodsComparisons
18 Aug 2018  Technique Narratives  Contributor(s): Jessica Libertini
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...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
Students will transform, solve, and interpret a tumor growth scenario using nonlinear 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...

6070SBeerBubbles
24 Apr 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
The goal of this project is to set up and numerically solve a firstorder 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...

FirstOrderModels
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Modeling with First Order EquationsMathematical models characterize physical systems, often using differential equations.Model Construction: Translating physical situation into mathematical terms. Clearly state physical principlesbelieved to govern process. Differential equation is a mathematical...

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Jessica Libertini
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...