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  1. 5-002-T-PhasePortraitForRelationshipDynamics

    15 Aug 2019 | Modeling Scenarios

    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. 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....

  3. 1-001c-S-PopulationDecayThenSome

    18 Jun 2019 | Modeling Scenarios

    This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

  4. 7-011-Text-T-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives

    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...

  5. 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...

  6. 7-011-Text-S-CoupledSystemLaplace

    31 Mar 2019 | Technique Narratives

    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...

  7. 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...

  8. 5090-T-SolidParticleErosion

    27 Mar 2019 | Modeling Scenarios

    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface. Examination of the solution will yield a formula for the...

  9. 1-143-S-PopulationModelVariationsMATLAB

    17 Feb 2019 | Modeling Scenarios

    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations.  They will also work with other utilities...

  10. 2008-Will-Hansen-ExamplesOfODEsInPhysics

    09 Dec 2018 | Potential Scenario Ideas

    Witt-Hansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

  11. 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...

  12. 2004-PhoebusReily-TheParachuteProblem

    09 Dec 2018 | Potential Scenario Ideas

    Phoebus, Ronald and Cole Reilly. 2004, Differential Equations and the Parachute Problem. Presentation 10 May 2004.  https://mse.redwoods.edu/darnold/math55/DEproj/sp04/coleron/presentation.pdf .Abstract: The parachute problem is a classical first semester differential equations problem...

  13. 1987-Rodin-Murthy-ComparativeEvalOfMathModelingBooks

    09 Dec 2018 | Potential Scenario Ideas

    Murthy, D. N. P. and E. Y. Rodin. 1987. A comparative evaluation of books on mathematical modeling. Mathematical Modeling. 9(1): 17-28.Abstract: In this paper we present a comparative evaluation of books on mathematical modelling that have appeared in the last 1.5 years.While dated this gives...

  14. 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...

  15. 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...

  16. 6-019-T-EnablingEpidemicExploration

    17 Sep 2018 | Modeling Scenarios

    We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.

  17. 6-019-S-EnablingEpidemicExploration

    17 Sep 2018 | Modeling Scenarios

    We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.

  18. 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...

  19. 6-003-T-SchoolFluEpidemic

    28 Aug 2018 | Modeling Scenarios

    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.

  20. 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.