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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.

    Keywords: simulationparameter estimationshoppingfittingbehaviour

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    THE IMPORTANCE OF GREEN SPACES & NATIVE PLANTS TO URBAN AVIFAUNA: A Lesson on how urban residential yards can support birds during their annual cycle
    In this lesson students will learn about the impacts of urbanization, and the conservation challenges it poses to wildlife, in particular avifauna. Introductory ecology topics such as the theory of...

    Keywords: birdsurbanizationPoisson Distributionnative plantsGeneralized linear models

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    3-043-BallisticModeling-SpongeDart-ModelingScenario
    The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.

    Keywords: projectile motionair resistanceballisticsdimensional analysisNewtonian mechanicssponge dartNerf gunNerf dartBuckingham's Theorem

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    2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
    In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.

    Keywords: SASsuperpositionpharmacokineticscompartmental modelsmultiple dose

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    1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
    Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two...

    Keywords: LSDcompartmentpharmacokinetics

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    1-104-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.

    Keywords: infectionlogisticexponentialcovidcarrying capacity

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    1-143-PopulationModelVariationsMATLAB-ModelingScenario
    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.

    Keywords: population dynamicsecologylogistic growthbifurcation theoryslope fieldsextinctionharvestingqualitative analysisstocking

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    2011-Lucas_Pulley-Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations
    This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare.

    Keywords: simulationpredator-preyLotka-VolterrapopulationCanadian LynxSnowshoe Harecritical values

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    2007-Ramsay-Hooker-Campbell-Cao-Parameter estimation for differential equations-a generalized smoothing approach
    We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations.

    Keywords: estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system

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    2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
    The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.

    Keywords: Fredholm integral equation ofLeontief’s modelmacroeconomic processes

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    2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
    Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without...

    Keywords: delayHIV-1T cellscombination antiviral therapy

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    How Luxury and Legacy Effects Shape Urban Avifauna in Los Angeles, California
    Is L.A.’s bird population shaped by historic redlining and income inequality? This lesson will introduce luxury and legacy effects hypotheses as they relate to urban avifauna in LA neighborhoods....

    Keywords: ANCOVASimple Linear Regressionurban ecologyredliningavian ecology

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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

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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with...

    Keywords: datalogisticracismprejudicemisinformationmemesspreaddisinformationinformationliesGoogle Trendscoinspennies

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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.

    Keywords: attritionLanchester modelpredator-predatorN-square Law

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    Quantifying Bacterial Growth in the Guts and Hemolymph of Fruit Flies: Mathematical Modeling and Data Interpolation/Extrapolation
    In this activity, students will analyze raw data obtained from an experiment that explores the effect of overexpressing the Ssk protein in order to strengthen the intestinal barrier and prevent...

    Keywords: graphingexponential growthlinear modelsqbccinterpolationConcepts in Statistics and Precalculus Understanding exponential rates and linear slopesExtrapolation

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    2020-TeachingModule-CarSuspension
    The modeling activity on car suspensions assumes that students have grappled with second order linear homogeneous differential equations with constant coefficients.

    Keywords: modulesuspensioncar suspensionsecond orderTeaching Module

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    5-001-LSD-ModelingScenario
    We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the...

    Keywords: LSDSpanishcompartmentpharmacokineticslysergic acid diethylamide

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    1-005C-OilSlick-ModelingScenario
    We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate.

    Keywords: Problem Solvingoil slickspreadfittinglineassumptions

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    1-001B-DeathImmigrationMystery-ModelingScenario
    We describe a classroom activity in which students use M\&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that...

    Keywords: m&mMystery Novelsimmigrationexperimentdeath

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