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    2011-Kurt_Kreith-The Mathematics of Global Change
    The authors discuss broad issues and then focus on specifics like exponential growth, logistic growth, and the logistic equation with delay.

    Keywords: exponential growthlogistic growth

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    2006-TK_Kar-Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge
    This paper deals with a prey–predator model incorporating a prey refuge and harvesting of the predator species.

    Keywords: survivalpredator-preyharvestrefugePontryagin’s maximal principlehidingoptimal harvest

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    1999-Peter_Deuflhard-Differential Equations in Technology and Medicine
    It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design.

    Keywords: cancerdesigntumordrugpolymertherapy

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    1989-Protopopescu-Santoro-Dockery-Combat modeling with partial differential equations
    We propose an extension of the classical modeling of combat via Lanchester equations to include one-dimensional spatial effects.

    Keywords: combatLanchester

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    Curvature and Maximum Permissible Speeds
    In this activity students will compute the curvature of a section of commuter rail and use it to determine a safe speed at which a train should can round the corner without tipping or derailing....

    Keywords: data analysiscalculusnumerical approximationengineeringcalculus 3transportation

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    1-003-IntroNumericalMethods-TechniqueNarrative
    We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions...

    Keywords: analytic solutionEuler's methodimproved Euler's method

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    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.

    Keywords: population dynamicsmalariaPolicyDecision-makingEuler's methodpharmacokineticsmosquitoimproved Euler's methodHuen's methodUS Army

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    1-062-BacteriaGrowth-ModelingScenario
    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential...

    Keywords: bacteriaexponentialgrowth

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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model...

    Keywords: zombiesSIR modelsGame

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    6-010-SocialCampaign-ModelingScenario
    The epidemic modeling problem is formulated as a system of three nonlinear, first order differential equations in which three compartments (S, I, and R) of the population are linked.

    Keywords: diseasegrowth rateJudgment and Decision MakingSIR modelinfections diseasesocial campaignrecovery ratedelay timejoining processquitting processexponential distribution

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    6-016-PandemicModeling-ModelingScenario
    The recent coronavirus outbreak has infected millions of people worldwide and spread to over 200 countries. How can we use differential equations to study the spread of coronavirus?

    Keywords: population dynamicsinfectious diseasediseaseEbolaeSIR modelsCOVID19pandemicepidemicreproduction number

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    The Impact of Climate Change on Sea Hare Respiration
    In this lesson, students interpret graphs of sea hare respiration. Then, students view and reflect on an interview with environmental scientist Dr. Richelle Tanner, who collected the data in the...

    Keywords: graph interpretationclimate changefmnBioGraphIrepresentation in STEMsea hare

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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...

    Keywords: stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates

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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle

    Keywords: Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error

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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...

    Keywords: Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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    Adapted Value of Mistakes
    This module is adapted from BIOMAAP materials on the value of mistakes and application of growth mindset in a microbiology lab.

    Keywords: growth mindsetmath attitudesResources @ BIOMAAPmistakesvalue of mistakes

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    Phenotypic plasticity and predation
    Students predict changes to tadpole morphology and coloration after considering characteristics of the predator species and the prey themselves then test their own hypotheses (typically with...

    Keywords: RExcelimage analysisgraphingt-testsfrequency histogramsdata visualizationANOVAhypothesis formulationpredator-prey interactionsphenotypic plasticity

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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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    2010-Kar-Chakraborty-Bioeconomic_modelling_of_a_prey_predator_system_using_differential_algebraic_equations
    We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response.

    Keywords: economicsbifurcationharvestfisheryequilibriumdifferential algebraic equation

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    5-026-Evictions-ModelingScenario
    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the...

    Keywords: carrying capacitycompartmentevictionhomeownerSIS modelhomelessness

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