
3092SWirelessPower
04 Aug 2021   Contributor(s):: Maila Hallare, Iordanka Panayotova
This activity presents an engineering application that is modelled by a coupled system of two linear secondorder differential equations with constant coefficients. One of the equations is homogeneous while the other one is nonhomogeneous. The application is called wireless power transmission...

6029STumorGrowth
04 Aug 2021   Contributor(s):: Allison Leigh Lewis
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

6017SOncolyticViruses
03 Aug 2021   Contributor(s):: Iordanka Panayotova, Maila Hallare
In this project, students explore oncolytic virotherapy using systems of differential equations and numerical simulations. The first activity guides the students in simulating the dynamics between the uninfected cancer cells x(t), the oncolytic virusinfected cancer cells y(t), and the...

5076SLanchesterLaws
27 Jul 2021   Contributor(s):: Blain Patterson
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In this project, you...

6026SFakingGause
30 Oct 2020   Contributor(s):: Brian Winkel
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.

5010SDNADegradation
21 Apr 2020   Contributor(s):: Brian Winkel
We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...

6045SCholeraTranmission
19 Apr 2020   Contributor(s):: Urmi GhoshDastidar
A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a...

6065SInternetPlatformUsers
30 Oct 2018   Contributor(s):: Victoria Rayskin
A model estimating the volume of users interacting through a twosided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

6024SDronePackageDelivery
18 Sep 2018   Contributor(s):: Eric Stachura, Rob Krueger
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 differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the analytical...

6003SSchoolFluEpidemic
28 Aug 2018   Contributor(s):: Darrell Weldon Pepper
We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

1108SPoissonProcess
27 Aug 2018   Contributor(s):: Mehdi HakimHashemi
In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

6007SFunctionsAndDerivativesInSIRModels
12 Aug 2018   Contributor(s):: Meredith L. Greer

6018SExploringSIRModel
30 May 2018   Contributor(s):: Ryan Edmund Miller, Stanley F Florkowski
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting SIR...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
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...

6040SStruggleForExistence
23 Nov 2016   Contributor(s):: Brian Winkel
We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters.

1029SConeToCubeFlow
02 Mar 2016   Contributor(s):: Sania Qureshi
We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom is suspended above an opentopped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

1027SStochasticProcesses
04 Jun 2015   Contributor(s):: Brian Winkel
We build the infinite set of first order differential equations for modeling a stochastic process, the socalled birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success. We work to build our model of random events which...