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    Modeling Scenario
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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
    Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order
    Technique Narrative
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    9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
    The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
    Maternal-Fetal interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers
    Modeling Scenario
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    1-059-ContainerShapeFallingWater-ModelingScenario
    We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
    containersTorricelli's Lawshapedischarge coefficient
    Modeling Scenario
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    270

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    1-001a-MMDeathImmigration-Variation-ModelingScenario
    We model exponential death with m&m's as well as death with immigration.
    simulationdatam&mimmigrationdeath
    Modeling Scenario
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    3-006-Buoyancy-ModelingScenario
    We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.
    data collectionexperimentbuoyancyNewton's Second Law of Motion
    Modeling Scenario
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    286

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    3-029-FerrisWheelCatch-ModelingScenario
    We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.
    parametric equationsprojectile motioninitial velocityferris wheelcatchcollision
    Modeling Scenario
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    3-060-DataToDifferentialEquation-ModelingScenario
    Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.
    Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation
    Modeling Scenario
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    3-076-CircuitBuilding-ModelingScenario
    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.
    simulationexperimentMultisimcircuitinductancecapacitorKirchhoff's Voltage Lawresistor
    Modeling Scenario
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    6-002-EulerCromerPendulum-ModelingScenario
    This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
    pendulumsemi-implicit methodsEuler-Cromernumerical solvers
    Modeling Scenario
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    3-150-ItsABlastFurnace-ModelingScenario
    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
    steady stateheat equationinverse problemfurnace
    Potential Scenario
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    73

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    2016-Manheim-EtAl-Improving Decision Support for Infectious Disease Prevention and Control
    This report describes decision-support tools, including models and nonmodeling approaches, that are relevant to infectious disease prevention, detection, and response and aligns these tools with real-world policy questions that the tools can help...
    infectious diseaseecosystemepidemicmodel policy
    Potential Scenario
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    2013-Deboeck-Bergeman-The reservoir model-DE model of psychological regulation
    The following article describes a differential equation model based on the concept of a reservoir for psychological regulation.
    adaptive copingReservoirsNotre Dame Longitudinal Study on Agingoutputinput distributionstressorscoping resources
    Potential Scenario
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    2003-Richard-Carson-Tracer kinetic modeling in PET
    The use of radiopharmaceuticals and the imaging of their biodistribution and kinetics with modern instrumentation are key components to successful developments in PET.
    Metabolismtomographyradiopharmaceuticalspositron emission
    Modeling Scenario
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    195

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    1-092-DashItAll-ModelingSenario
    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
    datarunningsprintHill-Kellerworld recordOlympics
    Modeling Scenario
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    1-160-HeartDeathRate-ModelingScenario
    Students simulate experience from a given data set which represents the heart death rate during the period 2000 - 2010 using several approaches to include exponential decay, difference equation, differential equation, and parameter estimation...
    dataheart death rate
    Modeling Scenario
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    5-015-RunnersSynchronize-ModelingScenario
    In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena.
    predatorAutonomous equationsoscillationcoupled oscillatorsynchronyrunnerpreyKuramato model
    Modeling Scenario
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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
    heat transferexperimentconductionconvectionboundary conditionsfinite volume method
    Modeling Scenario
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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.
    projectile motioninclined rampcoefficient of restitutionoptimal anglebounce
    Potential Scenario
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    2007-Bellomo-De_Angelis-Delitala-Lecture Notes on Mathematical Modelling in Applied Sciences
    The Lectures Notes correspond to the first part of the course devoted to modelling issues to show how the application of models to describe real world phenomena generates mathematical problems to be solved by appropriate mathematical methods.
    spring massLegendre polynomialsintegro-differential equationskinetic theory
    Free Online Textbook
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    2012-Vivek_Patel-Chemical Kinetics
    The book is designed to help the reader, particularly students, researchers, research scholars, scientists, chemists and industry fraternity of chemistry and allied fields; understand the mechanics and reactions rates.
    kineticschemistryreaction