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1-083-T-FallingMeteorites
24 Aug 2019 | Modeling Scenarios
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...
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9-010-T-TravelingWaves
21 Aug 2019 | Modeling Scenarios
In this scenario, students will be taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation (PDE) model, after a change of variables, students are led quickly to an ordinary differential equation (ODE) model. Students...
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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....
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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.
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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...
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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...
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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...
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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...
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1-063-T-ThreeHoleColumn
15 Dec 2018 | Modeling Scenarios
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.
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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...
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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...
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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...
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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.
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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.
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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.
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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.
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6-003-S-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.
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6-003-S-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.
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1-108-S-PoissonProcess
27 Aug 2018 | Modeling Scenarios
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.
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1-108-T-PoissonProcess
27 Aug 2018 | Modeling Scenarios
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.