
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...

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...

2001ChengTeachingMathematicalModeling
08 Sep 2017  Contributor(s):: Brian Winkel
Cheng, Ang Keng. 2001. Teaching mathematical modelling in Singapore schools. The Mathematics Educator. 6(1): 6375. Published by Association of Mathematics EducatorsFrom Introduction, “The purpose of this paper is to examine the possibility of introducing the teaching of mathematical...

1994DavisAskingGoodQuestionsAboutDEs
07 Sep 2017  Contributor(s):: Brian Winkel
Davis, Paul. 1994. Asking Good Questions about Differential Equations. The College Mathematics Journal. 25(5): 394400 A general essay about the Rule of Three – numerical, algebraic, and graphical perspectives + modeling with one illustration about Irish...

1975BurghesPopulationDynamics
07 Sep 2017  Contributor(s):: Brian Winkel
Burghes, David N. 1975. Population dynamics An introduction to differential equations. International Journal of Mathematical Education in Science and Technology. 6(3): 265276.Abstract: In this paper a number of population models, which lead to differential equations, are derived....

2006KarOptimalHarvestwithPreyRefuge
06 Sep 2017  Contributor(s):: Brian Winkel
Kar, Tapan Kumar. 2006: Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge. International Journal of Mathematical Education in Science and Technology. 37(5): 559571.Abstract: This paper deals with a prey–predator model...

2016deBoerModeling Population Dynamics Text
06 Sep 2017  Contributor(s):: Brian Winkel
De Boer, Rob J. 2016 Modeling Population Dynamics: A Graphical Approach. http://tbb.bio.uu.nl/rdb/books/mpd.pdf . Accessed 6 September 2017. 193 pp.From the Preface,“This book is an introduction into modeling population dynamics in ecology. Because there are several good...

2014deRossmodelingPopulationDynamicsText
05 Sep 2017  Contributor(s):: Brian Winkel
De Ross, Andre M. 2014. Modeling Population Dynamics. OnLine text. 222 pp. https://staff.fnwi.uva.nl/a.m.deroos/downloads/pdf_readers/syllabus.pdf . Accessed 4 September 2017From the Introduction to the text, “This course is intended as an introduction to the formulation, analysis...

2007LuoPopulation Modeling By Differential Equations
05 Sep 2017  Contributor(s):: Brian Winkel
Luo, Hui. 2007. Population Modeling by Differential Equations. Marshall University. Theses, dissertations and capstones. Paper 713. 31 pp. http://mds.marshall.edu/etd/713/ . Accessed 4 September 2017.Abstract: A general model for the population of Tibetan antelope is...