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    Potential Scenario
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    2009-G_Recktenwald-Tank Draining Exercise
    This paper describe deep mathematics, including differential equations concerned with modeling the draining of tank and the shape of the water coming out the bore hole at the bottom of the tank of water.
    laboratorytankLabViewBermoulli equationempty drainingcolumn of liquidpressure
    Modeling Scenario
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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
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    1-144-HeatCool-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
    temperatureNewton's Law of Coolingcooling
    Modeling Scenario
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    1-057-FiguringFluidFlow-ModelingScenario
    We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.
    dischargetankTorricelli's LawConservation of Energyfluid flowheightliquid
    Modeling Scenario
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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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    1-015-Torricelli-ModelingScenario
    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
    dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver
    Modeling Scenario
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    141

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    3-027-BobbingDropping-ModelingScenario
    We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
    drug resistancedirectedbuoyancyfree fallstatic equilibriumdisplacement
    Modeling Scenario
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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.
    concentrationdrug deliveryinner earcochleahearing loss
    Modeling Scenario
    289

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    3-009-BallDropInWater-ModelingScenario
    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
    resistancegravityfalling bodyterminal velocitybuoyancy
    Modeling Scenario
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    1-036-NeutralBuoyancy-ModelingScenario
    An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon
    DensitybuoyancyArchimedes’ Principlefloatneutral buoyance
    Technique Narrative
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    208

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    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
    bifurcationqualitative behaviorbifurcation diagram
    Modeling Scenario
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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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    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
    Free Online Textbook
    189

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    54

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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
    Modeling Scenario
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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.
    oscillationArchimedes’ Principlebuoancyoscillatory motionNewton's Second Law
    Potential Scenario
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    54

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    1994-JM_McDill-Bjorn_Felsager-The Lighter Side of Differential Equations
    Although differential equations have many serious applications to the modeling of real-world problems, a few lighthearted problems can serve to motivate students and brighten their attitudes toward a computer-oriented course in differential...
    cooperationharvestingRomeo and Julietlovecannibalismovercrowding
    Modeling Scenario
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    164

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    5-025-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
    compartmentsalttanks
    Potential Scenario
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    86

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    2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
    We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.
    projectstechnical writinginterdisciplinary skills
    Potential Scenario
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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.
    population dynamicslogisticLatter-Day Saints
    Potential Scenario
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    2003-Rasmussen-Keynes-Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations
    The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant...
    instructional designeigenvalueseigenvalue analysis