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    Modeling Scenario
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    1-060-SalesMarketing-ModelingScenario
    We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods against which models may be tested.
    marketingBass modelsalesconsumer productsinnovatorsimitators
    Modeling Scenario
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    1-136-MarriageAge-ModelingScenario
    Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these...
    messagesmarriageusing social sciences in forecastingdirected
    Potential Scenario
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    1999-Meyer-Ausubel-Carrying Capacity-A Model with Logistically Varying Limits
    This paper extends the logistic equation to simple growth model with a logistically increasing carrying capacity. This is applied to human population situations in several countries with fits to data.
    population dynamicsparameter estimationlimited growthgrowthlogisitic
    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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    2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
    In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
    logisticexponentialsigmoidtechnological innovationsasymptoticspread of innovation
    Modeling Scenario
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    1-125-DiceyPopulation-ModelingScenario
    We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the...
    simulationimmigrationdeathdice
    Modeling Scenario
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    6-009-FakeNews-ModelingScenario
    In modern society, creating and disseminating information is easier than ever. In this project, you will model the spread of fake news and investigate ways to deter distributing misinformation.
    sensitivity analysisSIR modelsSIS modelfake news
    Modeling Scenario
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    1-122-SpreadPEV-ModelingScenario
    We present data on world sales data of plug-in electric vehicles (PEVs) and request a model on the rate of change in sales over time, leading to prediction as to number of PEVs in the future.
    datalogisticpredictionspreadplug-in vehiclePEV
    General Resource
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    Instructor Solutions Second Edition SIMIODE Textbook HTML Version
    This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
    textbookhtmlSIMIODE textbookSecond Edition
    Potential Scenario
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    2014-Eckhoff-EtAl-Fun with maths-exploring implications of mathematical models for malaria eradication
    . In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches fomalaria eradication strategies.
    vaccinemalariamigrationeradicationseasonality
    Modeling Scenario
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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example.
    diseasecommon coldresidence hall
    Potential Scenario
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    54

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    1981-Nielsen-Rosenfeld-Substantive Interpretations of Differential Equation Models
    The use of differential equations models to study social processes has been increasing rapidly. There are, however, ambiguities in the interpretation of the parameters of these models.
    sociologypoliticsintragenerational mobilitypolitical mobility
    Modeling Scenario
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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.
    attritionLanchester modelpredator-predatorN-square Law
    Potential Scenario
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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.
    parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race
    Potential Scenario
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    2014-Do-Lee-A Differential Equation Model for the Dynamics of Youth Gambling
    We examine the dynamics of gambling among young people aged 16–24 years, how prevalence rates of at-risk gambling and problem gambling change as adolescents enter young adulthood, and prevention and control strategies.
    reproductive numberGamblingepidemicsensitivity indexyouth gambling
    Modeling Scenario
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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Potential Scenario
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    1994-JM_McDill-Bjorn_Felsager-The Lighter Side of Differential Equations
    Although differential equations have many serious applications to the modeling of real-world problems, a few lighthearted problems can serve to motivate students and brighten their attitudes toward a computer-oriented course in differential...
    cooperationharvestingRomeo and Julietlovecannibalismovercrowding
    Potential Scenario
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    2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
    We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.
    projectstechnical writinginterdisciplinary skills
    Modeling Scenario
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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Modeling Scenario
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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.
    population dynamicshumangrowth ratevarying growth rate