
1032SWordPropagation
07 Apr 2016   Contributor(s):: Rachelle DeCoste, Rachel Bayless
This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.

1029SConeToCubeFlow
02 Mar 2016   Contributor(s):: Sania Qureshi
We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom is suspended above an opentopped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

1055SWaterFallingInCone
27 Feb 2016   Contributor(s):: Brian Winkel
There are three videos associated with this Modeling Scenario and all are available on SIMIODE YouTube Channel: Capture3 YouTube Version SlowMoCapture1 YouTube Version SlowMoCapture2 YouTubeVersion and as streaming videos or down loads in this Modeling Scenario under the Supporting Docs Tab...

1021SFeralCatControl
24 Jan 2016   Contributor(s):: Rachel Bayless, Nathan Pennington
This activity is structured as a letter from a company seeking assistance with a mathematical problem. The students will act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use...

1034SFishMixing
24 Dec 2015   Contributor(s):: Eric Sullivan, Elizabeth Anne Carlson
This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a studentdesigned restocking and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...

1022SSpreadOfTechnology
27 Nov 2015   Contributor(s):: Brian Winkel
We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

2015Thoo, John  User Comments on SIMIODE 11M&M  Death and Immigration Modeling Scenario
21 Sep 2015   Contributor(s):: John Thoo
John Thoo, Department of Mathematics and Statistics, Yuba College, offers detailed narrative review on his use of this material

1992Bulte, C. H. F.  The differential equation of the deflection curve.
26 Jun 2015   Contributor(s):: C. H. F. Bulte
Bulte, C. H. F. 1992. The differential equation of the deflection curve. International Journal of Mathematical Education in Science and Technology. 23(1): 563.See https://www.tandfonline.com/doi/abs/10.1080/0020739920230106 .Article Abstract: This paper presents the derivation...

1977Mackey, Michael C. and Leon Glass  Oscillation and Chaos in Physiological Control Systems
26 Jun 2015   Contributor(s):: Michael C. Mackey, Leon Glass, William Clark
Mackey, Michael C. and Leon Glass. 1977. Oscillation and Chaos in Physiological Control Systems. Science. 197: 287289.See https://www.science.org/doi/abs/10.1126/science.267326 .Article Abstract: Firstorder nonlinear differentialdelay equations describing physiological control...

2015Goodnow, Jennifer, Richard Orr, and David Ross  Mathematical Models of Water Clocks.
25 Jun 2015   Contributor(s):: Jennifer Goodenow, Richard Orr, David Ross
Goodnow, Jennifer, Richard Orr, and David Ross. 2015. Mathematical Models of Water Clocks. 18 pp. http://www.nawccindex.net/Articles/GoodenowWaterClocks.pdf . Accessed 22 May 2015. Mathematics, Rochester Institute of Technology, Rochester NY USA.This is a historical tour of...

2010Panfilov, Alexander  NotesQualitative Analysis of Differential Equations
22 Jun 2015   Contributor(s):: Alexander Panfilov
Panfilov, Alexander. 2010. Qualitative Analysis of Differential Equations. 2010. Theoretical Biology, Utrecht University. 116 pp. http://wwwbinf.bio.uu.nl/panfilov/bioinformatica/bioinf10.pdf . Accessed 22 June 2015.This is a set of notes with derivations, motivating illustrations,...

2010Winkel, B. J.  Parameter estimates in differential equation models for chemical kinetics.
20 Jun 2015   Contributor(s):: Brian Winkel
Winkel, B. J. 2010. Parameter estimates in differential equation models for chemical kinetics. International Journal of Mathematical Education in Science and Technology. 42(1): 37 51.See https://www.tandfonline.com/doi/abs/10.1080/0020739X.2010.500806...

1011ASKinetics
06 Jun 2015   Contributor(s):: Karen Bliss
Adapted from 111Kinetics, SIMIODE modeling scenario. We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...

1027SStochasticProcesses
04 Jun 2015   Contributor(s):: Brian Winkel
We build the infinite set of first order differential equations for modeling a stochastic process, the socalled birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success. We work to build our model of random events which...

1026SEvaporation
04 Jun 2015   Contributor(s):: Brian Winkel
We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...

1025SMixingItUp
04 Jun 2015   Contributor(s):: Brian Winkel
Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

1023SRumorSpread
04 Jun 2015   Contributor(s):: Brian Winkel
We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.

1020SIceMelt
04 Jun 2015   Contributor(s):: Brian Winkel
We offer up the claim of a store catalog that its ice ball mold allows users to "... make ice balls that outlast cubes and won't water drinks down." We ask students to build a mathematical model to defend or contradict this claim.

1018SLogisticPopGrowth
04 Jun 2015   Contributor(s):: Brian Winkel
We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic model in these situations.

1017SDiseaseSpread
04 Jun 2015   Contributor(s):: Brian Winkel
We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways) in a differential equation model for the spread of the disease. Students ...