22 Jul 2020 | | Contributor(s):: Brian Winkel
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.
10 Jul 2020 | | Contributor(s):: Brian Winkel
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.
30 May 2020 | | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel
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 x-y-S-Title-StudentVersion-Czech.
29 May 2020 | | Contributor(s):: Brian Winkel
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.
21 Apr 2020 | | Contributor(s):: Brian Winkel
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 | | Contributor(s):: Brian Winkel
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...
04 Apr 2020 | | Contributor(s):: Brian Winkel
2011-Yafia-DEModelingMalignantTumorCellsInCompetitionWithImmuneSystemYAFIA, RADOUANE. 2011. A STUDY OF DIFFERENTIAL EQUATION MODELING MALIGNANT TUMOR CELLS IN COMPETITION WITH IMMUNE SYSTEM. International Journal of Biomathematics. 4(2): 185-206Abstract: In this...
2018-Joseph-Balamuralitharan - Nonlinear DE model of Asthma Effects
01 Apr 2020 | | Contributor(s):: Brian Winkel
2018-Joseph-Balamuralitharan - 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:...
01 Apr 2020 | | Contributor(s):: Brian Winkel
2007-RamseyEtAl-ParameterEstforDE-SmoothingApproachJ. 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....
26 Mar 2020 | | Contributor(s):: Brian Winkel
2015-Capaldi-SimulatingReiintroPassengerPidgeonBoggess, 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...
22 Mar 2020 | | Contributor(s):: Brian Winkel
2013-DeboeckEtAl-ReservoirModel-DEModelOfPsychRegulationDeboeck, P. R., & Bergeman, C. S. (2013). The reservoir model: A differential equation model of psychological regulation. Psychological Methods, 18(2), 237-256.Abstract: Differential equation models can be used to describe the...
2017-Ballard-Dice Activities for DE Models
20 Mar 2020 | | Contributor(s):: Brian Winkel
2017-Ballard-Dice 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 real-world scenario. Each can be used either...
09 Dec 2019 | | Contributor(s):: Don Hickethier
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...
31 Aug 2019 | | Contributor(s):: Bill Skerbitz
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...
28 Aug 2019 | | Contributor(s):: Kurt Bryan
This project introduces electrical resistivity tomography, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current. Specifically, a known electrical current is injected into an object (for example, the earth) and...
Ice Coverage in the Arctic Climate over time
17 Aug 2019 | | Contributor(s):: Wisam Victor Yossif Bukaita, Kelcey Meaney, Angie Dimopulos
In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...
Exploring differential equation of HIV infection
21 Jun 2019 | | Contributor(s):: Rebecca L. Goulson
Exploring differential equation models of the HIV infectionPresentation by Rebecca L. Goulson Department of Mathematics Pacific Lutheran University Tacoma, WA, May, 2015. 67 SlidesModels presented and data analyzed to determine parameters.
Jan 19 2019
Using Modeling to Motivate the Study of Differential Equations
AMS Special Session on Using Modeling to Motivate the Study of Differential Equations, IIRoom 336, BCC, 19 January 2019, 1:00 PM - 3:50 PMOrganizers:Robert Kennedy, Centennial High School, Ellicott...
10 Jan 2019 | | Contributor(s):: Brian Winkel
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.
15 Dec 2018 | | Contributor(s):: Brian Winkel
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.