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    Modeling Scenario
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    1-143-PopulationModelVariationsMATLAB-ModelingScenario
    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.
    population dynamicsecologylogistic growthbifurcation theoryslope fieldsextinctionharvestingqualitative analysisstocking
    Technique Narrative
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    1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
    Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
    carbon dioxideSurface Atmosphere Exchangebifurcationfold bifurcationsaddle node
    Potential Scenario
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    2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
    We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
    phytoplanktonbifurcationorbitsherbivorous zooplanktoneffect of fishmaturation time delay
    Modeling Scenario
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    1-135-FishHarvesting-ModelingScenario
    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the rate of harvesting fish.
    population dynamicsfishstabilitybifurcationharvest
    Technique Narrative
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    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
    bifurcationqualitative behaviorbifurcation diagram
    Potential Scenario
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    2014-Allen-EtAl-Perturbations in Epidemiological Models -When zombies attack we can survive
    In this paper, we investigate the existence of stability-changing bifurcations in epidemiological models used to study the spread of zombiism through a human population.
    epidemiologydynamical systemszombiesbifurcationperturbation
    Modeling Scenario
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    1-134-LanguageDynamics-ModelingScenario
    Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another.
    languagecompartmentphase linesbifurcationswitching
    Modeling Scenario
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    1-137-SheepGraze-ModelingScenario
    In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas for the herbivore consumption rate.
    herbivoreplantphase linesbifurcationoverexploitationsheepgraze
    Potential Scenario
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    2005-P_Howard-Modeling with ODE
    In these notes we consider three critical aspects in the theory of ordinary differential equations: developing models of physical phenomena, mathematically well-posed, solving ODE numerically .
    Fluid Mechanicscompartmentpopulationsvariational methodsHamiltonian mechanics
    Free Online Textbook
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    53

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    2017-Andrew_Lewis-Introduction_to_Differential_Equations_for_Smart_Kids
    The author addresses the question, "If I do not teach all of the usual techniques and tricks for solving differential equations, what do I replace it with?" in a number of wonderful ways.
    differential equationsmodelingtextbook
    Article or Presentation
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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow
    Technique Narrative
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    248

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    1-015-DimensionlessVariables-TechniqueNarrative
    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
    linearizationdimensional analysistime scalescalingdimensionless variablesspatial scale
    Potential Scenario
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    1994-T_Gruszka-A Balloon Experiment in the Classroom
    The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,
    resistancefalling bodydragballoon
    Modeling Scenario
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    1-079-HomeHeating-ModelingScenario
    This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
    Optimal Control TheorytemperatureheatfurnaceNewton's Law of Coolinghome heatingspecific heat
    Modeling Scenario
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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
    optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth
    General Resource
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    2003-Knorrenschild-Gross-Text Books on Mathematical Modeling in Biology
    Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild,
    biologyMathematical Biologytextbooktext
    Potential Scenario
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    2017-GR_Gustafson-Differential Equations Course Materials
    There are many applications from compartment and cascade analysis, recycling brine tank, home heating with multiple rooms, chemostat, microbes, heartbeats, lidocaine, nutrient flow in an aquarium, biomass transfer, pesticides, forecasting prices,...
    chemostatmicrobesbiomassforecastingtransfercompartmentpesticidesearthquaketankheatinglidocainebrineheartbeatsnutrient flowaquariumelectric networkscircuitsloggingbuildingcascade
    Potential Scenario
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    2008-Abramson-Mathematical modeling of the spread of infectious diseases
    These are informal notes, mostly based on the bibliography listed at the end and on recent papers in the field. The practical use of these models is based on the fact that they can be kept realistic enough.
    infectious diseaseepidemiccowpoxsmallpoxcomplex networks
    Modeling Scenario
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    1-115-ModelingWithFirstOrderODEs-ModelingScenario
    Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.
    bacteriafalling objectNewton's Law of Coolingdrugcoolingdrag
    Modeling Scenario
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    6-065-InternetPlatformUsers-ModelingScenario
    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system.
    dynamicsflowconservedfixed pointscycletinternet platformdiverghenceJacobianattractingrepellingnodesstablesaddlespiral