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1-142-S-WaterBottles
22 Aug 2021 | | Contributor(s):: Brody Dylan Johnson, Elodie Pozzi
This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version. The modeling scenario leads the students through an...
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3-069-S-HeatInBar
12 Aug 2021 | | Contributor(s):: Yuxin Zhang
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches. A series of experiments are designed to study the effects of materials, ambient fluid flows, geometric characteristics, and...
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3-076-S-CircuitBuilding
27 Jul 2021 | | Contributor(s):: Chiu Choi
In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closed-form solution...
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2007-Helfgott, Michel and Edith Seier - Some Mathematical and Statistical Aspects of Enzyme Kinetics.
05 Apr 2020 | | Contributor(s):: Brian Winkel
2007-HelfgottSeier-MathStatAspectsOfEnzymeKineticsHelfgott, Michel and Edith Seier. 2007. Some Mathematical and Statistical Aspects of Enzyme Kinetics. The Journal of Online Mathematics and Its Applications. Volume 7, October 2007, Article ID...
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2012-Transtrum, Mark K and Peng Qiu - Optimal experiment selection for parameter estimation in biological differential equation models.
02 Apr 2020 | | Contributor(s):: Brian Winkel
Transtrum, Mark K and Peng Qiu. 2012. Optimal experiment selection for parameter estimation in biological differential equation models. Bioinformatics. 13(181): 1-12.See https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-13-181...
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2006-MacWilliams, Matt - Developing Ordinary Differential Equations to Describe the Motion of a Paper Helicopter
15 Mar 2020 | | Contributor(s):: Brian Winkel
MacWilliams, Matt. 2006. Developing Ordinary Differential Equations to Describe the Motion of a Paper Helicopter. The Review: A Journal of Undergraduate Student Research. 8(8): 33-42.See https://fisherpub.sjfc.edu/ur/vol8/iss1/8/ .Abstract: Since George Box's...
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9-020-S-HeatDiffusion
14 Oct 2019 | | Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...
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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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2018-Bauer, Jessica and Eric Sullivan - Brewing the Perfect Cup of Tea with Differential Equations
18 Jan 2018 | | Contributor(s):: Eric Sullivan, Jesica A Bauer
Brewing the Perfect Cup of Tea with Differential EquationsBy Jesica Bauer and Eric Sullivan, Carroll CollegeA 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...
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2012-Urbano, Lensyl - The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus.
09 Oct 2017 | | Contributor(s):: Brian Winkel
Urbano, Lensyl. 2012. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus. Montessori Muddle.See http://montessorimuddle.org/2012/05/01/the-draining-of-a-jug-integrating-a-physics-experiment-into-calculus/ . Accessed 9 October 2017.Abstract: I...
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2017-Winkel, Brian - Experiences with Teaching Differential Equations in Context Using Modeling
25 Sep 2017 | | Contributor(s):: Brian Winkel
Brian Winkel, Director SIMIODE, gave a talk at Department of Mathematics, Seminar, at Clarkson University, Potsdam NY USA on 28 September 2017.Title: Experiences with Teaching Differential Equations in Context Using ModelingAbstract: We share experiences and examples of using modeling to...
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2003-Yildirim, Necmettin and Michael C. Mackey - Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data.
08 Sep 2017 | | Contributor(s):: Brian Winkel
Yildirim, Necmettin and Michael C. Mackey. 2003. Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data. Biophysical Journal. 84: 2841–2851. See https://pubmed.ncbi.nlm.nih.gov/12719218/...
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9-120-S-HorizontalBeam
22 Nov 2016 | | Contributor(s):: Gregg Waterman, Tiernan R Fogarty
This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions. Vertical deflection occurs as a result of the weight of the beam alone, with no compressive force at the ends or distributed...
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A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics
13 Oct 2016 |
Posted by Brian Winkel
James Puckett and Kimberly Spayd have authored a wonderful article in the current issue of PRIMUS with full citation:
Spayd, K. and J. Puckett. 2016. A Three-Fold Approach to the Heat Equation:...
https://simiode.org/blog/2016/10/a-three-fold-approach-to-the-heat-equation-data-modeling-numerics
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1-061-S-PotatoCooling
05 Oct 2016 | | Contributor(s):: Brian Winkel
We model the cooling of a baked potato and compare it to student-collected data.
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1-001B-S-MAndM-DeathImmigrationMystery
27 Jun 2016 | | Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice. Collected data on generation or iteration and population is then...
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1-028-S-SouthernSweetIcedTea
25 Jun 2016 | | Contributor(s):: Troy Henderson
We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.
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2010-Jungck, John R., Holly Gaff, and Anton E. Weisstein - Mathematical Manipulative Models: In Defense of "Beanbag Biology".
30 Jun 2015 | | Contributor(s):: John R. Jungck, Holly Gaff, Anton E. Weisstein
Jungck, John R., Holly Gaff, and Anton E. Weisstein. 2010. Mathematical Manipulative Models: In Defense of “Beanbag Biology”. CBE—Life Sciences Education. 9: 201–211.See https://www.lifescied.org/doi/pdf/10.1187/cbe.10-03-0040 .This paper offers up...
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2006-Ashline, George and Joanna Ellis-Monaghan - How high? How fast? How long? Modeling water rocket flight with calculus.
25 Jun 2015 | | Contributor(s):: Joanna Ellis-Monaghan, George Ashline
Ashline, George and Joanna Ellis-Monaghan. 2006. How high? How fast? How long? Modeling water rocket flight with calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 16(2): 121-137.See https://www.tandfonline.com/doi/abs/10.1080/10511970608984140...
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2014-Groetsch, C. W. and S. A. Yost - Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne.
20 Jun 2015 | | Contributor(s):: C. W. Groetsch, S. A. Yost
Groetsch, C. W. and S. A. Yost. 2014. Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne. The American Mathematical Monthly. 21(6): 499-505.Article Abstract: This article, inspired by a 17th-century woodcut, validates empirical observations of...