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    Modeling Scenario
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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
    Article or Presentation
    701

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    704

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    2020-TeachingModule-CarSuspension
    The modeling activity on car suspensions assumes that students have grappled with second order linear homogeneous differential equations with constant coefficients.
    modulesuspensioncar suspensionsecond orderTeaching Module
    Technique Narrative
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    165

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    5-012-LinearSystemConjecture-TechniqueNarrative
    Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
    discovery learningconjecturesolutionsubstitution
    Technique Narrative
    467

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    217

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    5-030-LinNonHomoSystemSol-TechniqueNarrative
    We offer strategies for solving linear systems of nonhomogeneous differential equations using a conjectured solution strategy for a system of constant coefficient, linear, n
    strategiesdiscovery learningeigenvectorseigenvalue
    Potential Scenario
    227

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    60

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    2014-Bozkurt-Peker-Mathematical modelling of HIV epidemic and stability analysis
    A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed. This model is analyzed by using the theory of both differential and difference equations to show the spread of HIV in a homogeneous population.
    diseaselogisticHIVpiecewise constantIndia
    Free Online Textbook
    194

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    63

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    2018-Mohammed_Kaabar-A_Friendly_Introduction_to_Differential_Equations
    In this book, there are five chapters: Laplace Transform, Systems of Homogeneous Linear Differential Equations, Methods of First and Higher Orders DEs, Extended Methods of First and Higher Orders DEs, and Applications of DEs.
    textbookordinary differential equations
    Modeling Scenario
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    126

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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
    433

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    263

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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
    DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law
    Modeling Scenario
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    180

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    3-051-ProjectileMotions-ModelingScenario
    We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
    trajectorylaunching radiantprojectile motionprojectileno resistanceangle of launch
    Modeling Scenario
    354

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    133

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    1-131-CaffeineElimination-ModelingScenario
    We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    caffeineeliminationpharmacokineticsdrug
    Modeling Scenario
    517

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    184

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    3-033-S-TimeUpTimeDown-ModelingScenario
    We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
    projectile motionapexvertical motion
    Modeling Scenario
    323

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    347

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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
    Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous
    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
    Article or Presentation
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    71

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    2009-Brian_Winkel-Population_modelling_with_MandMs
    Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.
    simulationparameter estimationimmigrationdeathdifference equation
    Free Online Textbook
    218

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    55

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.
    differential equationsmodelingtextbook
    Potential Scenario
    166

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    51

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    2018-Yu-Craciun-Mathematical_Analysis_of_Chemical_Reaction_Systems
    These models of chemical reactions are systems of coupled nonlinear differential equations on the positive orthant.
    biochemicalkineticsreactionreaction networkmass action
    Modeling Scenario
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    5-001-LSD-ModelingScenario
    We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.
    LSDSpanishcompartmentpharmacokineticslysergic acid diethylamide
    Modeling Scenario
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    1-070-FisheryHarvest-ModelingScenario
    Students model with logistic growth, harvesting, and diffusion in analyzing ocean fisheries of the Atlantic cod. We help students build models, ever more complex, to capture physical realities. At each stage we ask students to reflect on the model.
    logisticDiffusionmanagementharvestfishery
    Modeling Scenario
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    3-065-UpDown-ModelingScenario
    We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
    terminal velocityNewton's Second Law of Motionvelocitymotionapex
    Technique Narrative
    907

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    119

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    3-090-ChebyshevPolynomialSolution-TechniqueNarrative
    The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
    series soluotionpolynomial solutionsChebyshev polynomialsChebyshev differential equations