
1119SDairyFarming
20 Sep 2020   Contributor(s):: Rob Krueger
A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.

1096SOpAmpDifferentiator
09 Aug 2020   Contributor(s):: Virgil Ganescu
In this validationoriented setup, the output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and the results are compared with the data acquired from analyzing the numerical...

1088SRoomTemperature
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...

1136SMarriageAge
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 firstorder ordinary differential equations (which...

1128SRocketFlight
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.

1124SWorldPopulation
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 xySTitleStudentVersionCzech.

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...

1999McCartneyCareyModelingTrafficFlow
05 Apr 2020   Contributor(s):: Brian Winkel
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   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 HillKeller model for a...

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...

1001dSHotelPopulationDecay
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.

5005TextSStiffDifferentialEquations
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...

1003STextIntroNumericalMethods
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.

1063SThreeHoleColumn
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.

1062SBacterialGrowth
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...

1053SSlimeSpread
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.

7040STankInterruptMixing
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.

7020SThermometerInVaryingTempStream
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.

1138SInnerEarDrugDelivery
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 preclinical studies to examine local drug delivery to the cochlea. The...

2001TextSNumericalMethodsComparisons
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...