
2022KalmanImproved Approaches to Discrete and Continuous Logistic Growth
18 Mar 2022   Contributor(s):: Brian Winkel
2022. Kalman, Dan, Improved Approaches to Discrete and Continuous Logistic Growth. PRIMUS. Preprint at https://maa.tandfonline.com/doi/abs/10.1080/10511970.2022.2040664#.YjUMVurMI_U .Abstract: In the precalculus curriculum, logistic growth generally appears in either a discrete...

1005CSOilSlick
17 Jan 2022   Contributor(s):: Jennie D'Ambroise
We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate. This model enlightens students as to how derivatives are used in applications as well as a brief introductory encounter with parameter estimation for a linear,...

1160SHeartDeathRate
20 Sep 2021   Contributor(s):: Arati Nanda Pati
In this modeling scenario, we offer students simulation experience from a given data set which represents the heart death rate during the period 2000  2010 using several approaches to include exponential decay, difference equation, differential equation, and parameter estimation using EXCEL. We...

10100SInsectOutbreaks
17 Aug 2021   Contributor(s):: Jacob Paul Duncan
The mountain pine beetle (MPB, Dendroctonus ponderosae), a treekilling bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warmer weather has allowed MPB populations to achieve synchronous emergence and successful...

2014Bodine, Erin N.  Discrete Difference Equations.
26 Mar 2020   Contributor(s):: Brian Winkel
Bodine, Erin N. Discrete Difference Equations. Rhodes College. Notes. 37 pp. From, An Introduction to Discrete Mathematical Modeling"The field of mathematics provides many dierent means for modeling the world around us. Some mathematical toolsare...

2019Ekici, Celil and Chris Plyley  InquiryBased Modeling of Population Dynamics With Logistic Differential and Difference Equations
23 Mar 2020   Contributor(s):: Brian Winkel
Ekici, Celil and Chris Plyley. 2019. InquiryBased Modeling of Population Dynamics With Logistic Differential and Difference Equations. PRIMUS. 29(6): 553570. Freely available at the Mathematical Association of America Membership...

2018Sontag, Eduardo D  Lecture Notes on Mathematical Systems Biology
22 Mar 2020   Contributor(s):: Brian Winkel
Sontag, Eduardo D. 2018. Lecture Notes on Mathematical Systems Biology. 305 pp. See http://www.sontaglab.org/publications.html. Accessed 20 March 2020.The first version of these notes dates back to 2005. They were originally heavily inspired by Leah Keshet’s...

10001STilingHallway
12 Sep 2019   Contributor(s):: Rob Krueger, Eric Stachura
Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration. Then students will be introduced to the concept of the shift...

1001dSHotelPopulationDecay
03 Jul 2019   Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

1001cSPopulationDecayThenSome
18 Jun 2019   Contributor(s):: Dina Yagodich
This is an adaption of Modeling Scenario 1001SMandMDeathAndImmigration in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

1062SBacterialGrowth
15 Sep 2018   Contributor(s):: Arati Nanda Pati
We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

1108SPoissonProcess
27 Aug 2018   Contributor(s):: Mehdi HakimHashemi
In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

9001TextSSkinBurnModelNumericalMethods
18 Aug 2018   Contributor(s):: Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

1089SSpreadOfDisease
15 Aug 2018   Contributor(s):: Shinemin Lin
In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

1054SGrowthInFarmland
14 Aug 2018   Contributor(s):: Richard Spindler
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

2017Winkel, Brian  Dabbling in Differential Equation Modeling
25 Sep 2017   Contributor(s):: Brian Winkel
Brian Winkel, Director of SIMIODE, spoke on 27 September 2017 at a Noon gathering at the SUNY Potsdam School of Education and Professional Studies, Disciplined Inquiry in Education Seminar Series, organized by Dr. Sergei Abramovich School of Educaiton, SUNY Potsdam NY USA.Title: ...

2015Sayama, U.  Intro to Modeling and Analysis of Complex Systems
10 Sep 2017   Contributor(s):: Brian Winkel
Sayama, U. 2015. Intro to Modeling and Analysis of Complex Systems. Geneseo NY: Open SUNY Textbooks. 498 pp.Available at https://textbooks.opensuny.org/introductiontothemodelingandanalysisofcomplexsystems/ . Accessed 10 September 2017.From web site, “Introduction to the...

2014Bozkurt, Fatma and Fatma Peker  Mathematical modelling of HIV epidemic and stability analysis.
10 Sep 2017   Contributor(s):: Brian Winkel
Bozkurt, Fatma and Fatma Peker. 2014. Mathematical modelling of HIV epidemic and stability analysis. Advances in Difference Equations. 95.See http://www.advancesindifferenceequations.com/content/2014/1/95 . Accessed 10 September 2017.Abstract: A nonlinear mathematical...

2014Allen, Robert F., Cassandra Jens, and Theodore J. Wendt  Perturbations in Epidemiological Models: When zombies attack, we can survive!
09 Sep 2017   Contributor(s):: Brian Winkel
Allen, Robert F., Cassandra Jens, and Theodore J. Wendt. 2014. Perturbations in Epidemiological Models: When zombies attack, we can survive! Letters in Biomathematics. 1(2): 173180.See...

2017Tracy, Craig A.  Lectures on Differential Equations. Notes.
09 Sep 2017   Contributor(s):: Brian Winkel
Tracy, Craig A. 2017. Lectures on Differential Equations. Notes. 165 pp.See https://www.math.ucdavis.edu/~tracy/courses/math22B/22BBook.pdf . Accessed 7 September 2017.The author says,“These notes are for a onequarter course in differential equations. The approach is...