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    Modeling Scenario
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    1-083-FallingMeteorites-ModelingScenario
    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...
    falling object drag variable mass factor ranking meteor meteorite
    Modeling Scenario
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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
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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
    45

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    12

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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
    48

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    10

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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
    44

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    4

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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
    Modeling Scenario
    51

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    14

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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamics energy Fluid Mechanics m friction roller coaster integration by8 parts
    Modeling Scenario
    49

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    39

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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.
    population dynamics human growth rate varying growth rate
    Modeling Scenario
    36

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    16

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    1-130-AspirinAbsorption-ModelingScenario
    We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    pharmacokinetics drug aspirin
    Modeling Scenario
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    26

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    1-131-CaffeineElimination-ModelingScenario
    We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    caffeine elimination pharmacokinetics drug
    Modeling Scenario
    49

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    10

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    1-138-InnerEarDrugDelivery-ModelingScenario
    Students examine local drug delivery to the cochlea. The delivery system is modeled as a liquid mixing problem. Students formulate the differential equation, and solve the equation using separation of variables or integrating factor.
    concentration drug delivery inner ear cochlea hearing loss
    Modeling Scenario
    45

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    2

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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen M&M falling M up when tossed).
    Probability stochastic processes Bayesian methods probability distribution
    Modeling Scenario
    102

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    23

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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamics phage therapy exponential growth cancer water treatment decay surgery
    Modeling Scenario
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    11

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    1-190-IntroClass-ModelingScenario
    Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.
    population dynamics predator-prey logistic exponential graphical interpretations qualitative analysis
    Modeling Scenario
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    8

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    3-055-FloatingBox-ModelingScenario
    In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.
    oscillation Archimedes’ Principle buoancy oscillatory motion Newton's Second Law