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    A Momentum-First Approach to Newton’s Second Law
    Students frequently struggle with seeing the connection between forces and motion in introductory physics. This lesson is part of a combined momentum and kinematics unit that first teaches...

    Keywords: group workMomentumNewton's Laws

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    2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
    In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in...

    Keywords: population dynamicsecologydynamicsclassical mechanicschemical reaction

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    Effect of the Intestinal Protein Snakeskin on the Lifespan of Fruit Flies: A Kaplan-Meier Survival Analysissource Draft (1)
    In this activity, students perform the Kaplan-Meier survival analysis on raw data obtained from an experiment that explores the effect of overexpressing the Snakeskin (Ssk) protein on the lifespan...

    Keywords: graphingBiochemistryhypothesis testingcalculus and biologyapproximating areas under curvesqbccCellular and Molecular BiologyCreate graphsInterpret graphsSolving Equations and Inequalitiesinterpret tablesConcepts in Statisticsusing statisticschi-square analysissurvival analysis

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    Undergraduate data science: Biological connections and assessing impacts
    Presentation made by Lou Gross et al. as part of the "Bringing Research Data to the Ecology Classroom: Opportunities, Barriers, and Next Steps” Session at the Ecological Society of America...

    Keywords: Ecological Society of America

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    6-068-VisualizingPredator-PreyCycles
    In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be...

    Keywords: nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle

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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct...

    Keywords: dataphysicsdynamicsdata collectionrollingslippingripcordtoy

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    2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics
    This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.

    Keywords: projectileair resistancefree falldragharmonic oscillation

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    2017-ASHP-Intro to Pharmacokinetics and Pharmacodynamics
    This is the introductory Lesson 1 in an online set of materials to introduce Pharmacokinetics and Pharmacodynamics.

    Keywords: absorptioncompartmentbloodstreamplasmapharmacokineticspharmacodynamicstherapeutic concentration rangedrug dispositiondrug response

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    2013-Michael-Evans-Growth and Decay
    Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.

    Keywords: exponential growthexponential decayisotopespopulationsresource depletion

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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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    2009-Reid-King-Pendulum Motion and Differential Equations
    This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect...

    Keywords: pendulumphysical pendulum

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    2007-Helfgott-Seier-Some Mathematical and Statistical Aspects of Enzyme Kinetics
    We will analyze some basic ideas behind enzyme kinetics, which allow us to deal with separable and linear differential equations as well as realize the need to use power series.

    Keywords: kineticsEnzymeexperimental dataregresion

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    1-125-DiceyPopulation-ModelingScenario
    We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a...

    Keywords: simulationimmigrationdeathdice

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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...

    Keywords: instructional designeigenvalueseigenvalue analysis

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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.

    Keywords: pendulumFourier seriesTaylor seriesnumerical solution

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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

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    2009-Eriksson- Estep-Hansho-Johnson-Computational Differential Equations
    Differential Equations and Advanced Computational Differential Equations, presents a unified approach to computational mathematical modeling using differential equations based on a principle of a...

    Keywords: Galerkin

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    1999-F_Brauer-What Goes Up Must Come Down
    This paper is a wonderfully general analysis of the following, “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...

    Keywords: projectilefrictionfalling timerising timemaximum height

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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.

    Keywords: parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race

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    1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall
    We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.

    Keywords: fallingterminal velocityshuttlecockvertical fall

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