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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...

    Keywords: population modelparameter estimationpopulationparameter

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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.

    Keywords: simulationparameter estimationimmigrationdeathdifference equation

    207

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    60

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    1-034-T-FishMixing-ModelingScenario
    This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking...

    Keywords: simulationfishFishingmixingrestocking

    548

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    Translocation of Nutrients in the Phloem: Poiseuille's Equation
    This module introduces the Poiseuille equation in the context of understanding nutrient flow in plant cells. It is intended for an introductory biology audience.

    Keywords: plant physiologycalculushyperbolic equationsrates of change

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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.

    Keywords: microbiologyLotka Volterrramicrobiota

    227

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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.

    Keywords: sociologyarms racesaccumulative advantagealcoholismPeter Principlefemale mortalitypopulation pressureoccupational mobilitysocial mobilityRichardson theory of war

    120

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    Why does Blood Flow Change? Investigating the Math of Blood Flow Dynamics
    This collection of activities explores the relationship between blood flow, pressure, and the factors of resistance through graphs and modeling direct and inverse variation.

    Keywords: quant biographingRatiosmathassessmentcollege algebraundergraduate educationphysiologyAnatomyhuman biologyvariationCardiovascular physiologyAnatomy & Physiologylab activityOpenStaxqbccmanipulate equationsUnderstanding fractionsChoosing modelsUnderstanding ratesEstimating answersUse elementary functionsCreate graphsInterpret graphsRates and ProportionsSolving Equations and Inequalities

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    Necessary and Sufficient? Solving the Mystery of the Mitochondrial Pyruvate Transporter
    While there are several available lessons for teaching introductory biology students about diffusion, facilitated diffusion, and active transport, fewer materials exist to support upper-division...

    Keywords: DiffusionActive transportfacilitated diffusionNecessary and sufficientTransport proteins

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    2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
    The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the...

    Keywords: financedisabilitylife insurancemortalityinsuraneThiele’s equationBlack-Scholes equation

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    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify...

    Keywords: dynamical systemsregulationsteady statesales modelexternal stimulus

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    54

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    2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
    This article describes an equation of motion for a waggling pendulum.

    Keywords: resonanceinverted pendulummechanicsdamped pendulum

    105

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    56

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    2010-Shaza_Hussein-Predator-Prey Modeling
    The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible.

    Keywords: population dynamicspredator-preylogistic equationEndangered Catsdecreasing populationrabbitsfoxes

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    45

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    2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
    We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.

    Keywords: kineticschemical kineticszeroth order reactionfirst order reactionsecond order reaction

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    2001-Tsoularis-Analysis of logistic growth models
    variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. We further review and compare several such...

    Keywords: logisticGompertzVerhulstPearl and ReedBertalanffy

    120

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    2001-Edwards-Buckmire-A differential equation model of North American cinematic box-office dynamics
    A new mathematical model is presented for the box-office dynamics of a motion picture released in North America.

    Keywords: cinemamoviesbox-office

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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...

    Keywords: differential equationssimulationparameter estimationdifference equation

    250

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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...

    Keywords: differential equationstextbook

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    6-070-BeerBubbles-ModelingScenario
    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that...

    Keywords: molecular forensicsBEERspherebubbleNewton' Second LawIdeal Gas Lawdrag forceHadamardStokesmole

    278

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    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.

    Keywords: random perturbationBrownian motionLangevin equationRiemann-Steiltjes integralWiener processIto's calculus

    322

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    3-067-RLCSeriesCircuit-ModelingScenario
    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with...

    Keywords: resistanceMultisimcircuitRLC circuitinductancecapacitancecimulationgoverning equation

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