
1082TMirrorMirror
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...

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...

1068TWaterBottleCooling
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...

1001dTHotelPopulationDecay
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.

1107TClothDry
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...

5005TextTStiffDifferentialEquations
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...

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...

1125TDiceyPopulations
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...

1077TRLMSimSeriesCircuit
03 Mar 2019  Modeling Scenarios  Contributor(s): Jessica Libertini
In this validationoriented 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...

1042KoolAid 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 1042KoolAid. 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...

1003TTextIntroNumericalMethods
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...

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.

1063TThreeHoleColumn
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.

6024TDronePackageDelivery
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...

1062TBacterialGrowth
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...

6006TZombieGameHvZ
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 nonlinear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

1053TSlimeSpread
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.

1118TSolowEconomicGrowth
22 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
Students construct and analyze the celebrated SolowSwan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics, including elements of static optimization. Part one is...

7040TTankInterruptMixing
22 Aug 2018  Modeling Scenarios  Contributor(s): Jessica Libertini
We present a first order 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.

1138TInnerEarDrugDelivery
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....