
1082TMirrorMirror
21 Aug 2019  Modeling Scenarios
This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

1082SMirrorMirror
21 Aug 2019  Modeling Scenarios
This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

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....

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.

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...

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...

1003TTextIntroNumericalMethods
10 Jan 2019  Technique Narratives
We develop elementary approaches to numerically solving first order differential equations with Euler's Method and Improved Euler's Method. We ask students to develop these geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different...

1003STextIntroNumericalMethods
10 Jan 2019  Technique Narratives
We ask students to develop two numerical methods for solving first order differential equations geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.

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...

6024TDronePackageDelivery
18 Sep 2018  Modeling Scenarios
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...

6024SDronePackageDelivery
18 Sep 2018  Modeling Scenarios
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...

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.

6003TSchoolFluEpidemic
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.