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    Modeling Scenario
    391

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    265

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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
    Modeling Scenario
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    1-005-OilSlick-ModelingScenario
    We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
    model fittingspreadsheetsSpanishderrame de petróleodatosexpansiónoil slick
    Modeling Scenario
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    123

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    3-040-FirstPassageTime-ModelingScenario
    We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
    oscillatordampedunderdampedfirst passagefirst passage timespring mash dashpot
    Modeling Scenario
    247

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    181

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    1-064-TorricelliBox-ModelingScenario
    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.
    groundwater flowcolumn of waterTorricelli's Lawwater displacementsubmerged box
    Modeling Scenario
    266

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    253

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    1-052-SaltWaterTanks-ModelingScenario
    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.
    salttankmixing
    Potential Scenario
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    57

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    1986-Istvan_Gyori-Connections between compartment systems pipes and integro-differential equations
    In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given probability distribution functions.
    physiologypipelinecompartmentbloodcirculationintegro-differential equation
    Modeling Scenario
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    545

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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
    Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo
    Modeling Scenario
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    121

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    1-041-AirToTop-ModelingScenario
    One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using variable ascent rates.
    SCUBAascentair managementbreathingdivingunderwater
    Modeling Scenario
    335

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    136

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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
    229

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    151

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    6-028-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.
    concentrationcomparmentsalttankmixing
    Modeling Scenario
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    236

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    1-107-ClothDry-ModelingScenario
    We build a mathematical model for the rate of drying in a wet cloth while hanging in air. A model can be based on underlying physical principles (analytic) or based on observations and reasoned equations, but no physical assumptions (empirical).
    dryingclothevaporation
    Modeling Scenario
    279

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    186

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    1-025-MixingItUp-ModelingScenario
    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.
    compartmentsalttankmixing
    Potential Scenario
    119

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    70

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    2015-Goodnow-EtAl-Mathematical Models of Water Clocks
    This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.
    Torricelli's Lawwater clockBernoulli's Lawclepsydra
    Potential Scenario
    151

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    95

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    2014-John_Cimbala-Dynamic System Response
    In this learning module, we discuss the dynamic system response of sensors and their associated electronic circuits.
    sensor networksoscillationssystem responseelectronic circuit
    Potential Scenario
    201

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    54

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    2009-Shamim-EtAl-Investigating viscous damping using a webcam
    We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped, critically damped and underdamped regimes of harmonic motion.
    laboratoryunderdampedoverdampedcritically dampedharmonic motionimage processingviscous fluid
    Potential Scenario
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    54

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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment
    Technique Narrative
    399

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    195

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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
    Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time
    Modeling Scenario
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    180

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    1-039-StochasticPopModels-ModelingScenario
    We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.
    Probabilitypopulation dynamicsVarianceMeanstochasticdeterministic
    Modeling Scenario
    348

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    244

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    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
    optimizationpYield and sustainabilitynonprofit managementLaw of Mass Actionkineticreaction
    Modeling Scenario
    389

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    418

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    3-001-SpringMassDataAnalysis-ModelingScenario
    We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.
    datadampingspring-mass systemNewton's Second Law of Motionspring constantHooke's Law