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    Potential Scenario
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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
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    2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
    I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.
    in-class activityexperimentTorricelli's Lawcylinder of waterexpderiment
    Potential Scenario
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    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
    regressionlogisticTorricelli's Lawgrowthperiodic process
    Potential Scenario
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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
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    1992-Jude_Sommerfeld-More Applied Math Problems on Vessel Draining
    From a chemical engineering point of view emptying processing and storage tanks is important and this article considers many issues and shapes of containers. The main interest is in the total time it takes to empty the tank for a collection of...
    Torricelli's LawemptyTorricellivesselcontainer
    Potential Scenario
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    1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data
    With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations.
    circuitTorricelli's LawHooke's LawRC circuitharmonic oscillatorglucoseglucose tolerance test
    Potential Scenario
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    2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
    The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
    Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem
    Potential Scenario
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    2017-Bruce_Emerson-Wonderful World of Differential Equations
    This is a terrific set of noted with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of CoolingreactionsPoiseuille’s Lawstopping distancerate of changeproblemsmodeling opportunities
    Potential Scenario
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    2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
    This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of Coolingbiochemical reactionsPoiseuille’s Lawstopping distance
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    2018-Chris McCarthy-Newtons Law of Cooling
    You have hot water (initial temperature ) in a container, say a cup or glass. The temperature in the room is cooler, say a constant degrees Celsius. Come up with a differential equation that models the water's temperature.
    datawaterNewton's Law of Coolingcooling
    Potential Scenario
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    2017-Zhang-Wang-Study on public opinion propagation in self media age based on time delay differential model
    We establish the Logistic equation, introduce the operator time delay differential equation, and finally establish the improved delay differential equation, which can describe the propagation trend of network news from the self media.
    propagationpubic opinionNetwork public opinionpropagation lawself-mediaXiongan New Area
    Potential Scenario
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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
    kineticsbiochemical reactionreactantsproducts
    Potential Scenario
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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
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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    spring massoscillationHooke's Lawcoupled springsperiodicforcing functionphase portrait
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    2016-Pennell-Avitabile-White-Engineering Applications Differential Equations
    General discussion of an engineering based differential equations course with examples from RC Circuit, mass spring dashpot.
    circuitvoltagecapacitornondimensionalization
    Potential Scenario
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    2004-Denny-Yackel-Temperature Models for Ware Hall
    This paper offers some very nice extended models for cooling off a new office area for a mathematics department.
    Newton's Law of Coolingcoolingoffice building
    Potential Scenario
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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium
    Potential Scenario
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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing
    Potential Scenario
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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Potential Scenario
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    2017-David_Morin-Oscillations
    So needless to say, an understanding of oscillations is required for an understanding of waves.
    dampingfrequency responseresonanceoscillationbeatsunderdampingharmonic oscillatorsover dampingcritical damping