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  1. 5-002-T-PhasePortraitForRelationshipDynamics

    15 Aug 2019 | Modeling Scenarios | Contributor(s): Brian Winkel

    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....

  2. 7-011-Text-T-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives | Contributor(s): Brian Winkel

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  3. 7-011-Text-S-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives | Contributor(s): Brian Winkel

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  4. 1-109-T-EmployeeAttrition

    25 Mar 2019 | Modeling Scenarios

    This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

  5. 2017-Bonin EtAl - Math Modeling Based on ODE for Vaccinology

    09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Bonin, C.R.B. Et al. 2017. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Human Vaccines and Immunotherapy. 13(2): 484–489.Abtract: New contributions that aim to accelerate the development or to improve the efficacy and safety of...

  6. 6-024-T-DronePackageDelivery

    18 Sep 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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...

  7. 6-024-S-DronePackageDelivery

    18 Sep 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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...

  8. 6-006-T-ZombieGameHvZ

    09 Sep 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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 non-linear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

  9. 6-003-T-SchoolFluEpidemic

    28 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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.

  10. 6-003-S-SchoolFluEpidemic

    28 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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 | Modeling Scenarios | Contributor(s): Brian Winkel

    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. 1-108-T-PoissonProcess

    27 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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.

  13. 1-032-T-DigoxinElimination

    17 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

  14. 6-007-S-FunctionsAndDerivativesInSIRModels

    12 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

  15. 6-007-T-FunctionsAndDerivativesInSIRModels

    12 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases. The students view graphs both of solution curves and of the differential equations in the...

  16. 5-026-T-Evictions

    12 Aug 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

  17. 6-070-T-BeerBubbles

    24 Apr 2018 | Modeling Scenarios

    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...

  18. 6-070-T-BeerBubbles

    24 Apr 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    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...

  19. 2017-Allali-MathModelingOfAdaptiveImmunieResponses-HBVInfection

    07 Mar 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Karam Allali, Adil Meskaf, and Abdessamad Tridane. 2018. Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection. International Journal of Differential Equations. Volume 2017, Article ID 6710575, 13 pagesThis is an open access article distributed under the...

  20. 2003-RasmussenKeynes-LinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations

    03 Mar 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Rasmussen, Chris and  Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations.  PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...