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    2009-Marten-EtAl-Derivation and analysis of an ordinary differential equation for epilepsy dynamics
    In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations.

    Keywords: delayepilepsy dynamicsepilepsybistabilityseizure activity

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    1992-CHF_Bulte-The differential equation of the deflection curve
    This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general...

    Keywords: beamdeflectionshear forcebending momentcritical loadnatural frequency

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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.

    Keywords: phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation

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    9-010-TravelingWave-ModelingScenario
    Students are taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation model, after a change of variables, students...

    Keywords: traveling wavesseepage velocityporous medium

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    Parabolas Everywhere?
    In this lesson students will use mathematical models to describe real-world objects and to gain better understanding of quadratic functions.
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    2015-Just-Callender-Differential equation models of disease transmission
    The work give full analyses of standard epidemic model and then shows how to do it with differential equations and agent-based modeling. Then it compares the results.

    Keywords: disease transmissionSIR modelsepidemicagent-based

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    2015-Doust-Saraj-The logistic modeling population having harvesting factor
    The present paper deals with the logistic equation having harvesting factor, which is studied in two cases constant and non-constant.

    Keywords: logisticharvestharvesting factor

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    2012-Ogunrinde-Sunday-On some models based on second order differential equation
    This paper presents some models based on second order differential equations. Such models include interaction between different kinds of species in an environment and pricing policy for optimum...

    Keywords: species interactionpricing policyoptimal inventory

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    2012-Bech-EtAl-Resources For Engineering Applications Of Math
    Illustrations of applied mathematics including statics, truss, heat equation, column analysis, coupled oscillators, feedback control, AC circuit, chemical reactions, kinetics.

    Keywords: kineticsheat equationcolumn analysiscoupled oscillatorsfeedback controlAC circuitchemical reactions

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    1997-Bonnie_Shulman-Using Original Sources to Teach the Logistic Equation
    This Module uses original data, diagrams, and texts from three original sources to develop the logistic model of growth in natural systems with limited resources.

    Keywords: logisticoriginal source

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    1999-T_Chen-HL_He-GM_Church-S_Shafer-Modeling Gene Expression with Differential Equations
    The paper proposes and give great detail for a differential equation model for gene expression with two methods for constructing the model from a set of temporal data.

    Keywords: gene expressiongenekineticgene translationgene transcription

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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.

    Keywords: kineticsparameter estimationlogisticchemical kineticschemical reaction

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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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    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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    10-100-InsectOutbreaks-ModelingScenario
    We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.

    Keywords: ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave

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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

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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

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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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    2015-Dan_Sloughte-Notes on Diffy Qs Differential Equations for Engineers
    This is a calculus book with the last chapter devoted to ordinary differential equations topics. The effort begins with a study of numerical methods and goes through traditional technique strategies.

    Keywords: Numerical Methodspendulumtext

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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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