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    Article or Presentation
    196

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    2011-Brian_Winkel-Sourcing_for_parameter_estimation_and_study_of_logistic_differential_equation
    We present two simulation activities for students to generate real data and several data sources for the purpose of estimating parameters in the logistic differential equation model.
    dataparameter estimationparameterlogistic equationsource
    Article or Presentation
    189

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    48

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Population_Growth
    We estimate the parameters present in several differential equation models of population growth, specifically single species exponential and logistic growth, and multiple species competition and predation models.
    population modelparameter estimationpopulationparameter
    Article or Presentation
    186

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    67

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    2021-Brian_Winkel-Modelling_sublimation_of_carbon_dioxide
    We report results in our efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in our model.
    dataparameter estimationcarbon dioxidesublimationdry ice
    Article or Presentation
    195

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    71

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Chemical_Kinetics
    We estimate the parameters present in several differential equation models of chemical kinetics and logistic growth.
    kineticsparameter estimationlogisticchemical kineticschemical reaction
    Article or Presentation
    238

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    73

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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
    Article or Presentation
    281

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    85

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    2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
    An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.
    differential equationssimulationparameter estimationdifference equation
    Article or Presentation
    175

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    48

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    2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex
    We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their...
    exponential growthsolutionslinear systemsdecayconjecture
    Article or Presentation
    851

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    429

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    0

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    2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts
    We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.
    moduleoptimizationspring massmassspring\costTeaching Moduleminimal cost
    Article or Presentation
    249

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    532

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    2020-TeachingModule-ModelingNonlethalInfluenzaEpidemic
    We discuss the modeling efforts and tools for success in modeling the spread of nonlethal influenza in an English boarding school
    moduleepidemicboarding schoolTeaching Module
    Article or Presentation
    208

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    593

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    1

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    2020-TeachingModule-ModelingFallingColumnOfWater
    We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
    modulecolumn of waterTorricelli's LawTorricelliTeaching Module
    Article or Presentation
    133

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    65

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    0

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    1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change.
    datafirst orderparameterAIDS
    Article or Presentation
    258

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    632

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    2020-TeachingModule-ModelingSpreadOfOilSlick
    This is support material and video for teaching a Modeling Scenario using a first order ODE to model the spread of an oilslick with incomplete data.
    moduleoil slickTeaching Module
    Article or Presentation
    175

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    30

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    2013-Brian_Winkel-An_Optimal_Control_Model_in_Insect_Colonies
    we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at the end of a season.
    insect colonyoptimal controlparameter
    Article or Presentation
    171

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    55

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    1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall
    This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern equipment.
    parameter estimationdata collectionresistancefallingterminal velocityNewton's Second Law of Motionshuttlecock
    Article or Presentation
    174

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    56

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    0

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    2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution
    In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.
    ProbabilityMeanPoisson processbirth and death processinfinite number of differential equations
    Article or Presentation
    163

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    68

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    0

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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.
    differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility
    Article or Presentation
    137

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    49

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    1999-F_Brauer-What_Goes_Up_Must_Come_Down
    It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces that are nonlinear functions of velocity.
    resistancefallingprojectilevertical projectile
    Article or Presentation
    201

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    94

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    SIMIODE Spring 2024 Webinars - WikiModel
    WikiModel is cloud-based application and requires no installation and is run via a web-browser to facilitate rapid implementation. Equations are typed in as they appear in a textbook. ODEs are automatically integrated via Runge-Kutta methods.
    modelingSoftwaretoolapplicationWikiModelmodeling cycle
    Article or Presentation
    195

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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
    Article or Presentation
    144

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    57

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    2001-A_Tsoularis-Analysis_of_logistic_growth_models
    The paper presents an historical development of the logistic equation in its various forms, including Verhulst, Pearl and Reed, Gompertz, Bertalanffy, Richards, and others.
    logisticpopulationgrowth curvelimited growthGompertzhistorylogistic equationVerhulstPearl and ReedBertalanffyRichards