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1-092-S-DashItAll
01 Sep 2019 | | Contributor(s):: Kurt Bryan
This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a...
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1-084-S-GoingViral
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...
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9-015-S-UnearthingTruth
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...
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3-150-S-ItsABlastFurnace
13 Aug 2019 | | Contributor(s):: Kurt Bryan
This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...
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3-130-S-MatterOfSomeGravity
07 Aug 2019 | | Contributor(s):: Kurt Bryan
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or...
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1-107-S-ClothDry
27 Apr 2019 | | Contributor(s):: Brian Winkel
We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...
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1-125-S-DiceyPopulations
04 Mar 2019 | | Contributor(s):: Brian Winkel
We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...
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3-043-S-BallisticModeling-SpongeDart
20 Nov 2018 | | Contributor(s):: Jean Marie Linhart, Peter Howard
The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance. The first two models are based respectively on the common simplifying assumptions of no air resistance and...
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6-019-S-EnablingEpidemicExploration
17 Sep 2018 | | Contributor(s):: Brian Winkel
We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.
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1-053-S-SlimeSpread
30 Aug 2018 | | Contributor(s):: Brian Winkel
We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.
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1-141-S-M&MGameRevisited
27 Aug 2018 | | Contributor(s):: Mehdi Hakim-Hashemi
In this project students will learn to find a probability distribution using the classical M&M game in SIMIODE.
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Two competing populations: simulations with differential equations
01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan
Abstract: Suppose two populations are competing with each other. How can they then develop? We offer insights with simulation calculations. In the model is the evolution of the biomass of the two populations described with differential equations. A fundamental building block is the logistic...
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Wandi Ding - Experience and Lessons Learned from Using SIMIODE Modeling Scenarios
19 Jan 2018 | | Contributor(s):: Wandi Ding
Experience and Lessons Learned from Using SIMIODE Modeling ScenariosBy Wandi Ding, Ryan Florida, Jeffrey Summers, Puran Nepal, Middle Tennesse State UniversityA talk given at the AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution at...
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Bill Skerbitz - The Logic of Logistics
19 Jan 2018 | | Contributor(s):: Bill Skerbitz
The Logic of LogisticsBy Bill Skerbitz, Wayzata High SchoolA talk given at the AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13 January 2018
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Dan Teague - Comparing Simulations with Solutions for Classical Differential Equation Models
18 Jan 2018 | | Contributor(s):: Dan Teague
Comparing Simulations with Solutions for Classical Differential Equation Models By Daniel J. Teague, North Carolina School of Science and Mathematics A talk given at the AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution at...
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2000-deOliveraEtAl-PinholeWaterFlowFromCylindricalBottles
26 Nov 2017 | | Contributor(s):: Brian Winkel
2000. deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite. Pinhole Water Flow From Cylindrical Bottles. Phys.Educ. 35(2): 110-119.From the opening of the article, "We performed an experiment on elementary hydrodynamics. The...
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2012-Urbano-The Draining of a Plastic Bottle
09 Oct 2017 | | Contributor(s):: Brian Winkel
2012-Urbano, Lensyl. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus. Montessori Muddle. http://montessorimuddle.org/2012/05/01/the-draining-of-a-jug-integrating-a-physics-experiment-into-calculus/ . Accessed 9 October 2017.Abstract: I punched a small hole...
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1971-BoyesEtal-Lidocaine In Man
09 Oct 2017 | | Contributor(s):: Brian Winkel
Boyes, R. N., D. B. Scott, P. J. Jebson, M. J. Godman, and D. G. Julian, M.D. 1971. Lidocaine in Man. Clinical Pharmacology and Therapeutics. 12(1): 105-116.Abstract: Plasma levels of lidocaine were measured in 5 normal male volunteers following both intravenous and oral administration of...
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Ramsay-From Data To Differential Equations
23 Sep 2017 | | Contributor(s):: Brian Winkel
Ramsay, Jim. From Data To Differential Equations. Presentation. 52 slides.Themes:Differential equations are powerful tools for modeling data.There are new methods for estimating differential equations directly from data.Some examples are offered, drawn from chemical engineering and...
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2011-CaoEtAl-Robust Estimation for Ordinary Differential Equation Models
23 Sep 2017 | | Contributor(s):: Brian Winkel
Cao, J., L. Wang, J. Xu. 2011. Robust estimation for ordinary differential equation models. Biometrics. 67(4): 1305-13.Abstract: Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine and...