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    Modeling Scenario
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    1-096-OP-AMP-Differentiator-ModelingScenario
    The output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and compared with the data acquired from numerical model (using...
    simulation Measurement feedback Multisim circuit voltage operational amplifier validation SPICE
    Modeling Scenario
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    48

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    1-098-NeuronDetection-ModelingScenario
    Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in mathematical neuroscience as ``integrate-and-fire''...
    biology neuroscience neuron physiology voltage integrate and fire threfhols coincidence detection RC circuit
    Modeling Scenario
    105

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    24

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    1-100-EngineeringDemographics-ModelingScenario
    Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women in the United...
    logistic population Improved Euler Method Gompertz demographics women autonomous
    Modeling Scenario
    117

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    48

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    1-101-ClassMMDeathImmigration-ModelingScenario
    We offer students an opportunity to generate unique data for their team on a death and immigration model using m&m's and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters.
    simulation immigration data collection death
    Modeling Scenario
    117

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    44

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
    optimization logistic prediction data fitting power law Gompertz cancer growth eponential Bertalanaffy
    Modeling Scenario
    109

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    30

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
    optimization cancer logistic exponential prediction tumor growth data fitting power law Bertanffy Gompertz
    Modeling Scenario
    94

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    14

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    1-104-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.
    infection logistic exponential covid carrying capacity
    Modeling Scenario
    94

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    21

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    1-105-AnimalFall-ModelingScenario
    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
    animal Netwon's Second Law of Motion falling body terminal velocity air resistance Newton air friction fall
    Modeling Scenario
    105

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    65

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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the sun heats the water. Students model the tide pool's...
    data snails temperature Newton's Law of Cooling cooling Newton warming tital pool tide pool
    Modeling Scenario
    104

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    35

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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with a separable linear first order differential...
    data logistic racism prejudice misinformation memes spread disinformation information lies Google Trends coins pennies
    Modeling Scenario
    90

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    29

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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
    climate energy temperature linearization phase lines energy balance model root finding
    Modeling Scenario
    94

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    14

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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.
    bacteria falling object Newton's Law of Cooling drug cooling drag
    Modeling Scenario
    72

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    29

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    1-116-TropicalStormWindspeeds-ModelingScenario
    We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential equation using a first order exponential decay model.
    hurricane decay tropical storm cyclones
    Modeling Scenario
    95

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    11

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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.
    optimization economics steady state growth Solow-Swan model capital production labor Golden Rule of Economic Growth
    Modeling Scenario
    84

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    11

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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.
    population dynamics dairy farmers' markets growth cow