
3064TGearTrain
31 Aug 2019  Modeling Scenarios
In this scenario students will model an inputoutput mechanical system of gears with a second order, nonhomogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components. Students should have some...

5002TPhasePortraitForRelationshipDynamics
15 Aug 2019  Modeling Scenarios
The different possible dynamics of a twoperson 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....

3150TItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

3150SItsABlastFurnace
13 Aug 2019  Modeling Scenarios
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

1001cSPopulationDecayThenSome
18 Jun 2019  Modeling Scenarios
This is an adaption of Modeling Scenario 1001SMandMDeathAndImmigration 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.

3067TRLCSeriesCircuit
28 Apr 2019  Modeling Scenarios
In this validationoriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).

7011TextTCoupledSystemLaplace
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...

7011TextSCoupledSystemLaplace
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...

5090TSolidParticleErosion
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...

5090TSolidParticleErosion
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...

1109TEmployeeAttrition
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 firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

5005TextTStiffDifferentialEquations
05 Mar 2019  Technique Narratives
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

5005TextSStiffDifferentialEquations
05 Mar 2019  Technique Narratives
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

1143SPopulationModelVariationsMATLAB
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...

3009TBallDropInWater
16 Dec 2018  Modeling Scenarios
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

2008WillHansenExamplesOfODEsInPhysics
09 Dec 2018  Potential Scenario Ideas
WittHansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

2004PhoebusReilyTheParachuteProblem
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...

1987RodinMurthyComparativeEvalOfMathModelingBooks
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): 1728.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...

6019TEnablingEpidemicExploration
17 Sep 2018  Modeling Scenarios
We offer several strategies for estimating parameters in models of epidemics, one using a MichaelisMenten saturation infected rate.

6019SEnablingEpidemicExploration
17 Sep 2018  Modeling Scenarios
We offer several strategies for estimating parameters in models of epidemics, one using a MichaelisMenten saturation infected rate.