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    1991-Thoddi_Kotiah-Difference and differential equations in the mathematics of finance
    Many problems arising in the mathematics of finance involve identical money flows at regular time intervals and are typically solved by appropriate valuation at a focal date or by setting up an...

    Keywords: financesavingsgrowth fundinterestmortgageannuitydepreciation

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    1992-Jude_Sommerfeld-More Applied Math Problems on Vessel Draining
    From a chemical engineering point of view emptying processing and storage tanks is important and this article considers many issues and shapes of containers. The main interest is in the total time...

    Keywords: Torricelli's LawemptyTorricellivesselcontainer

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    1977-Michael_Mackey-Leon_Glass-Oscillation and Chaos in Physiological Control Systems
    First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle...

    Keywords: sensitivitychaosparametersRespirationdelayblood cells

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    2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick
    An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and...

    Keywords: differential equationssimulationparameter estimationdifference equation

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    6-070-BeerBubbles-ModelingScenario
    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that...

    Keywords: molecular forensicsBEERspherebubbleNewton' Second LawIdeal Gas Lawdrag forceHadamardStokesmole

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    1-030-EyeModel-ModelingScenario
    We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region...

    Keywords: retinal surgeryAkaike Information CriterionSpanishsum of square errorssurgeryretionaophthalmologyeyeintraocular gas bubble

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    1-005-OilSlick-ModelingScenario
    We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order,...

    Keywords: model fittingspreadsheetsSpanishderrame de petróleodatosexpansiónoil slick

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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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    1-097-SwimmingPool-ModelingScenario
    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.

    Keywords: concentrationcchlorinenumerical errorswimming poolhorineerreor

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    1-022-SpreadOfTechnologies-ModelingScenario
    We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic...

    Keywords: data analysistechnologylogisticspreadinnovation

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    1-011A-Kinetics-ModelingScenario
    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.

    Keywords: kineticsLaw of Mass Actionfittingorder of reactionchemical reaction

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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through...

    Keywords: Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo

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    1-060-SalesMarketing-ModelingScenario
    We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods...

    Keywords: marketingBass modelsalesconsumer productsinnovatorsimitators

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    1-077-RLMSimSeriesCircuit-ModelingScenario
    In this validation setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data...

    Keywords: MeasurementcircuitvoltagecurrentvalidationSPICERL circuitMultilsim

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including ...

    Keywords: optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including...

    Keywords: optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz

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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the...

    Keywords: datasnailstemperatureNewton's Law of CoolingcoolingNewtonwarmingtital pooltide pool

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    1-115-ModelingWithFirstOrderODEs-ModelingScenario
    Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.

    Keywords: bacteriafalling objectNewton's Law of Coolingdrugcoolingdrag

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    1-001a-MMDeathImmigration-Variation-ModelingScenario
    We model exponential death with m&m's as well as death with immigration.

    Keywords: simulationdatam&mimmigrationdeath

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    6-023-DroneHeadingHome-ModelingScenario
    We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.

    Keywords: dronesoursuitflight pathchange of variables

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