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    Technique Narrative
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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
    Transformationspower series
    Free Online Textbook
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    2021-G_Nagy-Ordinary_Differential_Equations
    This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations.
    differential equationstextbook
    Modeling Scenario
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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
    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
    Potential Scenario
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    2019-Stender_EtAl-Recovery_Of_Differential_Equations_From_Impulse_Response
    In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation.
    time seriesregressionresponseimpulseoscillationsignal processingsparse regressionsystem identification
    Modeling Scenario
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    1-077-RLMSimSeriesCircuit-ModelingScenario
    In this validation setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using...
    MeasurementcircuitvoltagecurrentvalidationSPICERL circuitMultilsim
    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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    2011-Kenny_Harwood-Modeling a RLC Circuit Current with Differential Equations
    This paper gives an abbreviated description of the photovaltaic effect (solar power production process) and then a RLC circuit will be modeled that is powered by a photovaltaic panel.
    tuningfrequency responseLC circuitRLC
    Modeling Scenario
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    4-055-ShatterWineGlass-ModelingScenario
    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?
    frequencydampingamplituderesonanceoscillationshatteringwine glassbridgesaircraftexternal force
    Modeling Scenario
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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
    resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket
    Potential Scenario
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    2002-Faia-Differential Equation Modeling as a Source of Theoretical Insight-Four Disparate Examples
    We explore differential equations involving alcoholism, social mobility, excess female mortality, and international arms competition.
    sociologyarms racesaccumulative advantagealcoholismPeter Principlefemale mortalitypopulation pressureoccupational mobilitysocial mobilityRichardson theory of war
    Potential Scenario
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    1994-T_Gruszka-A Balloon Experiment in the Classroom
    The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,
    resistancefalling bodydragballoon
    Article or Presentation
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    2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling
    This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues.
    modulelinear systemsdigoxinTeaching Module
    Potential Scenario
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    2019-Hu-Treinen-One-step_method_for_modelling_longitudinal_data_with_differential_equations
    This study proposes a new approach to estimate the parameters in differential equation models used to describe non-linear trajectories of longitudinal data.
    simulationparameter estimationshoppingfittingbehaviour
    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
    Potential Scenario
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    1999-Peter_Deuflhard-Differential Equations in Technology and Medicine
    It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design.
    cancerdesigntumordrugpolymertherapy
    Technique Narrative
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    5-010-MatrixExponential-TechniqueNarrative
    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and...
    matrix esponentialPutzer's Algorithmdiagonalizationeigenvalueseigenvectors
    Modeling Scenario
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    1-079-HomeHeating-ModelingScenario
    This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
    Optimal Control TheorytemperatureheatfurnaceNewton's Law of Coolinghome heatingspecific heat
    Modeling Scenario
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    4-020-AnIEDBlast-ModelingScenario
    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use the model to determine the results of a dynamical...
    applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces
    Article or Presentation
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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
    circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit