
1096SOpAmpDifferentiator
09 Aug 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
In this validationoriented setup, the output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and the results are compared with the data acquired from analyzing the numerical...

3105SFrequencyResponse
22 Jul 2020  Modeling Scenarios
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

3027SBobbingDropping
10 Jul 2020  Modeling Scenarios
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.

1088SRoomTemperature
15 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

1136SMarriageAge
11 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are firstorder ordinary differential equations (which...

1128SRocketFlight
04 Jun 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

1124SWorldPopulation
30 May 2020  Modeling Scenarios
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be xySTitleStudentVersionCzech.

1124SWorldPopulation
30 May 2020  Modeling Scenarios  Contributor(s): Jessica Libertini
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be xySTitleStudentVersionCzech.

3026SSpringInverseProblem
29 May 2020  Modeling Scenarios
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

5010SDNADegradation
21 Apr 2020  Modeling Scenarios
We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...

Transient and Steady State response in RC or RL circuits
16 Apr 2020  Presentations
Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides, This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

Transient and Steady State response in RC or RL circuits
16 Apr 2020  Presentations  Contributor(s): Jessica Libertini
Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides, This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

1999McCartneyCareyModelingTrafficFlow
05 Apr 2020  Potential Scenario Ideas  Contributor(s): Jessica Libertini
1999McCartneyCareyModelingTrafficFlowMcCartney, Mark and Malachy Carey. 1999. Modelling Traffic Flow: Solving and Interpreting Differential Equations. Teaching Mathematics and its Applications: An International Journal of the IMA. 18(3):...

2011YafiaDEModelingMalignantTumorCellsInCompetitionWithImmuneSystem
04 Apr 2020  Potential Scenario Ideas
2011YafiaDEModelingMalignantTumorCellsInCompetitionWithImmuneSystemYAFIA, RADOUANE. 2011. A STUDY OF DIFFERENTIAL EQUATION MODELING MALIGNANT TUMOR CELLS IN COMPETITION WITH IMMUNE SYSTEM. International Journal of Biomathematics. 4(2): 185206Abstract: In this...

2018JosephBalamuralitharan  Nonlinear DE model of Asthma Effects
01 Apr 2020  Potential Scenario Ideas
2018JosephBalamuralitharan  Nonlinear DE model of Asthma EffectsJoseph ,G Arul J. and S Balamuralitharan. 2018. A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM. IOP Conf. Series: Journal of Physics: Conf. Series. 1000:...

2007RamseyEtAlParameterEstforDESmoothingApproach
01 Apr 2020  Potential Scenario Ideas
2007RamseyEtAlParameterEstforDESmoothingApproachJ. R. Statist. Soc. B (2007)69, Part 5, pp. 741–796Ramsay, J. O.. G. Hooker, D. Campbell and J. Cao. 2007. Parameter estimation for differential equations: a generalized smoothing approach. J. R. Statist. Soc....

2015CapaldiSimulatingReiintroPassengerPidgeon
26 Mar 2020  Potential Scenario Ideas
2015CapaldiSimulatingReiintroPassengerPidgeonBoggess, Erin, Jordan Collignon, and Alanna Riederer. 2015. Mathematical Modeling in Ecology: Simulating the Reintroduction of the Extinct Passenger Pigeon (Ectopistes migratorius).Valparaiso University. Abstract: The...

2013DeboeckEtAlReservoirModelDEModelOfPsychRegulation
22 Mar 2020  Potential Scenario Ideas
2013DeboeckEtAlReservoirModelDEModelOfPsychRegulationDeboeck, P. R., & Bergeman, C. S. (2013). The reservoir model: A differential equation model of psychological regulation. Psychological Methods, 18(2), 237256.Abstract: Differential equation models can be used to describe the...

2017BallardDice Activities for DE Models
20 Mar 2020  Potential Scenario Ideas
2017BallardDice Activities for DE ModelsIntroduction: This document includes descriptions of four activities that are appropriate for a calculus or differential equations class, all using dice to motivate a differential equation model for a realworld scenario. Each can be used either...

2005TextSLinearizeItAll
09 Dec 2019  Technique Narratives
Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained. A simple model using Torricelli's Law will compare the exact solution to...