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    Modeling Scenario
    161

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    96

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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
    Potential Scenario
    83

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    50

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    2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
    A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
    delaytime delystep response
    Potential Scenario
    75

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    31

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    1999-Leonid_Hanin-Which tank empties first
    Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
    tankTorricelli's Lawspherical tankemptyfrustrum of conecylinder
    Potential Scenario
    139

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    34

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    1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
    A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
    plantoscillationdelaycircumnutationturning
    Potential Scenario
    154

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    41

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    2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics
    This provides an excellent step-by-step of the physiology, construction of model, and notions like peak concentration as well as issues like lag time.
    concentrationphysiologydrugslag timeExtravascularPharamacokineticspeak time
    Potential Scenario
    132

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    50

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    0

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    2016-Starling-EtAl-Local Brewery - A Project for Use in Differential Equations Courses
    We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer.
    BEERFermentationbrewery
    Modeling Scenario
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    1983

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    3-030-SecondOrderIntro-ModelingScenario
    We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
    parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight
    Potential Scenario
    233

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    43

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    2012-Hassan_Moore-Using projects to stimulate learning in mathematics and engineering mathematics courses
    Given that time is a premium in the academy and project creation is a time consumer, three original projects, which may be injected into any Calculus III, Differential Equations, or Engineering Mathematics course, have been created.
    solutionsclass projectsphysical phenomenon
    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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    262

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    1-061-PotatoCooling-ModelingScenario
    We model the cooling of a baked potato and compare it to student-collected data.
    least sum of square errorsNewton's Law of Coolingcoolingpotato
    Article or Presentation
    143

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    60

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    0

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    1994-Brian_Winkel-Ant_Tunnels_and_Calculus
    A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.
    differential equationsdifference equationfirst orderderivative definitionant tunnel
    Potential Scenario
    119

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    38

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    1971-Boyes-Scott-Jebson-Godman-Julian-Lidocaine in Man
    Plasma levels of lidocaine were measured in 5 normal male volunteers following both intravenous and oral administration of the drug.
    pPharmacologypharmacokineticslidocaine
    Article or Presentation
    92

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    42

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    2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
    The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
    Newton's Law of Coolingtime of deathdouble exponentialcoroner
    Article or Presentation
    154

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    410

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    1

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    2020-TeachingModule-ModelingFallingColumnOfWater
    We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
    modulecolumn of waterTorricelli's LawTorricelliTeaching Module
    Potential Scenario
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    59

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    2017-Anders_Kallen-Single species models in continuous time
    Part of a series of Lecture notes this lecture contains rich materials on logistic harvest models, spruce budworms, and chemostat.
    chemostatlogisticharvestspruce budworm
    Potential Scenario
    113

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    34

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Article or Presentation
    212

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    53

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    0

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    2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
    An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.
    differential equationssimulationparameter estimationdifference equation
    Technique Narrative
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    138

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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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    161

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    1-063-ThreeHoleColumnOfWater-ModelingScenario
    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.
    fallingcolumn of waterTorricelli's Lawmultiple spigotsspigots
    Modeling Scenario
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    1-090-EmptySphericalTank-ModelingScenario
    We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
    VolumesphereTorricelli's Lawtimingspherical tankfluidempty