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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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    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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    3-076-CircuitBuilding-ModelingScenario
    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.

    Keywords: simulationexperimentMultisimcircuitinductancecapacitorKirchhoff's Voltage Lawresistor

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    3-150-ItsABlastFurnace-ModelingScenario
    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.

    Keywords: steady stateheat equationinverse problemfurnace

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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more...

    Keywords: diseasecommon coldresidence hall

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    2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
    The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest...

    Keywords: Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem

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    2006-Juska-Gedminiene-Ivanec-Growth of Microbial Populations-Mathematical Modeling-Laboratory Exercises-Model-Based Data Analysis
    The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous...

    Keywords: population growth ratelogistic equationVerhulst equationgeneration timelag time

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    1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
    The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.

    Keywords: kineticsnonlinear regressionsum of square errorsMonodlinearizemineralizationsubstratescarbonaceous

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    1-006-Financing-ModelingScenario
    We describe two situations, one in which we are saving for a purpose and one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation...

    Keywords: financesavingsloaninterest ratepayment

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    Developmental Allometry: Scaling in Growth
    This Excel workbook illustrates a number of allometric equations in animal growth. The workbook also calculates an allometric equation with graphical output for data entered by the user.

    Keywords: allometrybrain developmentSkeletal Systemmetabolic rate

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    2017-William_Bialek-Boxes and Arrows To Differential Equations
    This material uses pictures to build kinetic models of reactions and then offers analytic solutions.

    Keywords: Michaelis-MentenEnzymesubstrateDNA\kinetis

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    2017-Floyd_Ballard-Dice Activities for DE Models
    This document includes descriptions of four activities that are appropriate for a calculus or differential equations class, all using dice to motivate a differential equation model for a real-world...

    Keywords: simulationcurve fittingcdicecollect dataclass activitiesanalyze dataclass activity

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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer...

    Keywords: cancertumorfittingagent-based

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    2015-Beckmann-Sanchez-Cache Calculus-Modeling Caches through Differential Equations
    We present cache calculus, a technique that models cache behavior as a system of ordinary differential equations, letting standard calculus techniques find simple and accurate solutions of cache...

    Keywords: discretecachecache calculus

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    2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
    I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.

    Keywords: in-class activityexperimentTorricelli's Lawcylinder of waterexpderiment

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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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    2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
    In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.

    Keywords: logisticexponentialsigmoidtechnological innovationsasymptoticspread of innovation

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    2008-Yang-EtAl-Differential Equation Model of HIV Infection of CD T-Cells with Delay 
    Abstract: An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time...

    Keywords: virusT cellsHopf bifurcationendemic equilibrium

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    2006-Han-EtAl-Ordinary differential equation models for ethanol pharmacokinetic based on anatomy and physiology
    Physiologically-based pharmacokinetic (PBPK) models have been used to describe the distribution and elimination characteristics of intravenous ethanol administration.

    Keywords: liverwortsintraveneouspharmacokineticsethanolethanol infustionpharmacodynamictissue model

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    2005-Saifullah-Mathematical Modeling With Differential Equations
    This article aims to provide the students some basic modeling skills, which will have applications to a wide variety of problems.

    Keywords: species interactionsword equationinteractive software

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