Tags: system

Modeling Scenarios (1-17 of 17)

  1. 3-092-S-WirelessPower

    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 second-order differential equations with constant coefficients. One of the equations is homogeneous while the other one is non-homogeneous. The application is called wireless power transmission...

  2. 6-029-S-TumorGrowth

    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...

  3. 6-017-S-OncolyticViruses

    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 virus-infected cancer cells y(t),  and the...

  4. 5-076-S-LanchesterLaws

    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...

  5. 6-026-S-FakingGause

    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.

  6. 5-010-S-DNADegradation

    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...

  7. 6-045-S-CholeraTranmission

    19 Apr 2020 | | Contributor(s):: Urmi Ghosh-Dastidar

    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...

  8. 6-065-S-InternetPlatformUsers

    30 Oct 2018 | | Contributor(s):: Victoria Rayskin

    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

  9. 6-024-S-DronePackageDelivery

    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...

  10. 6-003-S-SchoolFluEpidemic

    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.

  11. 1-108-S-PoissonProcess

    27 Aug 2018 | | Contributor(s):: Mehdi Hakim-Hashemi

    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.

  12. 6-007-S-FunctionsAndDerivativesInSIRModels

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

  13. 6-018-S-ExploringSIRModel

    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...

  14. 6-070-S-BeerBubbles

    24 Apr 2018 | | Contributor(s):: Michael Karls

    The goal of this project is to set up and numerically solve a first-order 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...

  15. 6-040-S-StruggleForExistence

    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.

  16. 1-029-S-ConeToCubeFlow

    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 open-topped 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...

  17. 1-027-S-StochasticProcesses

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We build the infinite set of first order differential equations for modeling a stochastic process, the so-called 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...