
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.

1109SEmployeeAttrition
25 Mar 2019   Contributor(s):: Lyle Clifford Smith
This scenario models the loss of employees and the employer's attempt to retain them through stock options. This is intended for introductory students and is paired well with exponential growth/decay material. We also introduce the 5% rule to sort possible factors into assumptions and...

1986CookeLinear And Logistic Harvesting ModelsMath Modeling Journal
09 Dec 2018   Contributor(s):: Brian Winkel
Cook, K. L. and M. Witten. 1986. Onedimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301340.Abstract: Some of the results in the literature on simple onedimensional, density dependent, discrete and continuous modelswith and without harvestingare reviewed. Both...

6006TZombieGameHvZ
09 Sep 2018   Contributor(s):: Jue Wang
Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of nonlinear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

1067SModelingWithSigmoidCurves
18 Aug 2018   Contributor(s):: Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

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...

Population Modeling
01 Mar 2018   Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan
This paper offers many problems inolving a single population model while introducing several specific models. Both numerical methods and qualitative anlyses are offered.The paper is in German and is entitled, "Populationsmodelle: Eine Einführung in Differentialgleichungen."Hans R....

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018   Contributor(s):: Michael Karls
Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913...

2012LevermoreOrdinaryDifferentialEquationsGraphical MethodsApplications
01 Dec 2017   Contributor(s):: Brian Winkel
Levermore. David. 21012. FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp/5. FirstOrder Equations: General Theory5.1. WellPosed Problems 25.2. Existence and Uniqueness 36. FirstOrder Equations: Graphical Methods6.1....

2010HusseinPredatorPreyModeling
26 Nov 2017   Contributor(s):: Brian Winkel
2010. Hussein, Shaza. PredatorPrey Modeling. Undergraduate Journal of Mathematical Modeling: One + Two. 3(1): Article 20. http://scholarcommons.usf.edu/ujmm/vol3/iss1/32 . Accessed 27 November 2017.Abstract. Predatorprey models are useful and often used in the environmental...

2015EndaleApplicationsOfODEsToRealWorldSystems
26 Nov 2017   Contributor(s):: Brian Winkel
2015. Endale, Mersha Amdie. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the physical...

Math 216 Demonstrations
12 Sep 2017   Contributor(s):: Brian Winkel
Math 216 Demonstrations. https://instruct.math.lsa.umich.edu/lecturedemos/ma216/docs/ . Accessed 11 September 2017.This site contains many, many applications with good presentation and analysis as well as Matlab files to illustrate the concepts. For example modeling a swinging door with spring...

Logistic Equation Harvesting Variations
12 Sep 2017   Contributor(s):: Brian Winkel
Logistic Equation Harvesting Variations. Activitues. 5 pp.This is a set of descriptions of various logistic models are offered. Keywords: differential equation, model, harvest, constant harvest, varying harvest , disease, extinction, explosion, population, restocking

2000IdelsWangHarvesting fisheries management strategies with modified effort function
12 Sep 2017   Contributor(s):: Brian Winkel
Idels, Lev. V. and Mei Wang. 2000. Harvesting Fisheries Management Strategies With Modified Effort Function . Int. J. Modelling, Identification and Control. Preprint.Abstract: In traditional harvesting model a fishing effort E is defined by the fishing intensity and does not address the inverse...

2010SteinworthEtAl modeling a fish population and the effects of overfishing
12 Sep 2017   Contributor(s):: Brian Winkel
Steinworkth, Bailey, Yuhui Wand, Xing Zhang. 2010. Modeling of a Fish Population and the Effects of Overfishing. Student Project. James Madison University. 22 pp.Abstract: According to the United Nations, 200 million people depend on fishing as their source of food or livelihood.1 However,...

Verhulst Population Model with Harvest
11 Sep 2017   Contributor(s):: Brian Winkel
Verhulst Population Model with HarvestNotes. 20 pp.Building on the Verhulst model of limited growth there are a number of problems and solutions offered, including issues of harvesting.Keywords: differential equation, model, problems, solutions, Verhulst, population, harvest,

2005HowardModeling with Differential Equations
10 Sep 2017   Contributor(s):: Brian Winkel
Howard P. 2005. Modeling with ODE. Notes. 48 pp.Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are...

2010ClementiDelCielloHart Modeling Disease
10 Sep 2017   Contributor(s):: Brian Winkel
Del Ciello, Sarah, Jack Clementi, and Nailah Hart. 2010. Modeling Disease – FinalReport. http://educ.jmu.edu/~strawbem/math_201/final_reports/Clementi_DelCiello_Hart_Final.pdf . Acessed 8 September 2017.Abstract: This paper models the progression of a disease through a set population...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017   Contributor(s):: Brian Winkel
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.Abstract: Differential equation models for population dynamics are now standard fare in singlevariable calculus. Building on these ordinary differential equation (ODE)...

PennelDifferential Equaitons First Order Applications
09 Sep 2017   Contributor(s):: Brian Winkel
Pennel, Steve. Differential Equations: Applications of First Order Differential Equations. Notes. 44 p. Universiyt of Massachusetts, Lowel.This is a set of modeling activities with derivations, Matlab code, and mathematical details covering the following topics: Newton’s Second Law...