
1142SWaterBottles
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...

3069SHeatInBar
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...

3076SCircuitBuilding
27 Jul 2021   Contributor(s):: Chiu Choi
In this project students will establish a mathematical model for an electric circuit as a secondorder ordinary differential equation with constant coefficients. They will derive the initial conditions for this differential equation by using circuit laws. They will obtain its closedform solution...

2007Helfgott, Michel and Edith Seier  Some Mathematical and Statistical Aspects of Enzyme Kinetics.
05 Apr 2020   Contributor(s):: Brian Winkel
2007HelfgottSeierMathStatAspectsOfEnzymeKineticsHelfgott, 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...

2012Transtrum, 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): 112.See https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471210513181...

2006MacWilliams, 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): 3342.See https://fisherpub.sjfc.edu/ur/vol8/iss1/8/ .Abstract: Since George Box's...

9020SHeatDiffusion
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...

1053SSlimeSpread
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.

2018Bauer, 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, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego...

2012Urbano, 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/thedrainingofajugintegratingaphysicsexperimentintocalculus/ . Accessed 9 October 2017.Abstract: I...

2017Winkel, 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...

2003Yildirim, 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/...

9120SHorizontalBeam
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...

A ThreeFold 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 ThreeFold Approach to the Heat Equation:...
https://www.simiode.org/blog/2016/10/athreefoldapproachtotheheatequationdatamodelingnumerics

1061SPotatoCooling
05 Oct 2016   Contributor(s):: Brian Winkel
We model the cooling of a baked potato and compare it to studentcollected data.

1001BSMAndMDeathImmigrationMystery
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...

1028SSouthernSweetIcedTea
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.

2010Jungck, 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.10030040 .This paper offers up...

2006Ashline, George and Joanna EllisMonaghan  How high? How fast? How long? Modeling water rocket flight with calculus.
25 Jun 2015   Contributor(s):: Joanna EllisMonaghan, George Ashline
Ashline, George and Joanna EllisMonaghan. 2006. How high? How fast? How long? Modeling water rocket flight with calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 16(2): 121137.See https://www.tandfonline.com/doi/abs/10.1080/10511970608984140...

2014Groetsch, 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): 499505.Article Abstract: This article, inspired by a 17thcentury woodcut, validates empirical observations of...