
9020THeatDiffusion
14 Oct 2019  Modeling Scenarios
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

9020SHeatDiffusion
14 Oct 2019  Modeling Scenarios
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

1092TDashItAll
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...

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...

1084TGoingViral
31 Aug 2019  Modeling Scenarios
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...

1084SGoingViral
31 Aug 2019  Modeling Scenarios
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...

1083TFallingMeteorites
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 (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

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...

1076TClimateBifurcation
08 Aug 2019  Modeling Scenarios
In this paper we present (for educational purposes) simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a ``Venus type of climate.'' The models are accompanied by Matlab...

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...

SCUDEM and COMAP MCM/ICM Talk at University of Nebraska  Lincoln
22 Apr 2019  CompetitionsSCUDEM
Elizabeth Carlson, holder of NSF Graduate Research Fellowship at the University of Nebraska  Lincoln, Lincoln NE USA, gave a talk in the spring 2018 to the mathematics club at her school on Math Modeling Competitions. Enjoy!

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...

AMS Special Session on Using Modeling to Motivate the Study of Differential Equations  JMM 2019, Baltimore MD USA
20 Jan 2019  Presentations
We offer the presentation for AMS Special Session on Using Modeling to Motivate the Study of Differential Equations, I in Room 336, BCC, 19 January 2019, 8:00 AM 11:50 AM held at the Joint Mathematics Meetings 2019, Baltimore MD USAAs we assemble them the presentations are...