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    Technique Narrative
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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
    Potential Scenario
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    2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus
    We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.
    calculusFlightprojectilewater rocket
    Modeling Scenario
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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.
    Polynomial dynamical systembeamcantilever
    Potential Scenario
    165

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    54

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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
    Technique Narrative
    373

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    187

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    1-003-IntroNumericalMethods-TechniqueNarrative
    We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions and compare them to analytic solutions.
    analytic solutionEuler's methodimproved Euler's method
    Technique Narrative
    460

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    211

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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
    Technique Narrative
    605

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    242

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    1-001-SepartionOfVariables-TechniqueNarrative
    We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
    solutionsstrategymethodapplications
    Potential Scenario
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    2002-Fay-The Pendulum Equation
    We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it.
    pendulumFourier seriesTaylor seriesnumerical solution
    Modeling Scenario
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    10-001-TilingHallway-ModelingScenario
    Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift operator.
    Geometryiterationtilingrecurrenceshift operatorpatternsclosed formanalytic solution
    Modeling Scenario
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    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
    exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano
    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
    Potential Scenario
    167

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    60

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    2006-Michael_Coleman-Population Modeling with Ordinary Differential Equations
    We will investigate some cases of differential equations population models beyond the separable case and then expand to some basic systems of ordinary differential equations.
    population dynamics
    Potential Scenario
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    2007-Hui_Luo-Population Modeling by Differential Equations
    A general model for the population of Tibetan antelope is constructed. The present model shows that the given data is reasonably logistic.
    population dynamicsextinctionlogisticTibetan antelope
    Free Online Textbook
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    2015-Dan_Sloughte-Notes on Diffy Qs Differential Equations for Engineers
    This is a calculus book with the last chapter devoted to ordinary differential equations topics. The effort begins with a study of numerical methods and goes through traditional technique strategies.
    Numerical Methodspendulumtext
    Article or Presentation
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    2012-R_B_Ogunrinde-J_Sunday-On_some_models_based_on_second_order_differential_equations
    This paper presents some models based on second order differential equations. This is a very straightforward article with good explanations of modeling assumptions.
    combatcombat modelspecies interaction
    Technique Narrative
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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
    computationerrorTorricelli's Lawdata fittinglinear approximation
    Technique Narrative
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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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    1-054-GrowthInFarmland-ModelingScenario
    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...
    fittingfarmfarmland
    Modeling Scenario
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    1-083-FallingMeteorites-ModelingScenario
    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...
    falling objectdragvariable massfactor rankingmeteormeteorite
    Modeling Scenario
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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
    slope fieldspopulation