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    Potential Scenario
    160

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    55

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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
    Technique Narrative
    419

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    200

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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
    394

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    194

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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
    431

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    839

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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
    sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank
    Potential Scenario
    221

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    71

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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates
    Modeling Scenario
    383

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    250

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    1-097-SwimmingPool-ModelingScenario
    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.
    concentrationcchlorinenumerical errorswimming poolhorineerreor
    Modeling Scenario
    261

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    113

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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle
    Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error
    Modeling Scenario
    214

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    214

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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of second order differential equations to model a planet
    optimizationsum of square errorsvector calculusLagrange multipliersline integrals
    Modeling Scenario
    217

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    228

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
    Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error
    Potential Scenario
    219

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    51

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    1999-Khorasheh-Ahmadi-Gerayeli-Application of Direct Search Optimization for Pharmacokinetic Parameter Estimation
    For simple pharmacokinetic compartmental models, analytical solution to the governing differential equations provide a mean to evaluate the associated rate constants. Such methods, however, can not be used used for more complex multi-compartment...
    sum of square errorsleast squarespharmacokineticslineteicscompartmental modelsdirect search
    Potential Scenario
    812

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    52

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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
    Free Online Textbook
    210

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    50

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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