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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which...

    Keywords: Trigonometric Functionscirclesquigonometryinverse functiontrigonmetry

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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which...

    Keywords: TrigonometryTrigonometric Functionsparametric equationscirclesinecosinesquigonometryinverse function

    118

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    25

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    0

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of...

    Keywords: goal functionabsolute error curvesinvers methodholling-Tanner model

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    2005-Albert_Tarantola-Inverse Problem Theory and Methods for Model Parameter Estimation
    This is a bible of approaches to support parameter estimation approaches in inverse problems. Theory and algorithms are offers with examples.

    Keywords: Algorithminverse probleminverse

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    2007-Zenker-Rubin-Clermont-From inverse problems in mathematical physiology to quantitative differential diagnoses
    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data...

    Keywords: physiologyinverse problem

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    2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
    This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes...

    Keywords: sustainabilityfishFishingmanagementharvestfisherstrategyoverfishing

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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.

    Keywords: Transformationspower series

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    2009-Martinez-Luaces-Modelling Applications Inverse Modelling
    The discussion in this paper will deal with non-typical inverse problems and how they can be used in engineering courses.

    Keywords: Laplace transforminverse problemtankmixinginverse

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    7-010-MultipleDoses-ModelingScenario
    Two multiple dose drug administration regimens are offered. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus...

    Keywords: drug discoverystep functiondoseDiracdrug administrationinverse Laplace Transformintraveneousbolussteady drip

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    2007-Graham-Lerch-Parameter Recovery for a Differential Equation Model
    This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models and electrical circuit.

    Keywords: laboratorydata collectionRLC circuitinvers problemelectrical circuit

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    3-026-SpringInverseProblem-ModelingScenario
    We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

    Keywords: datamassinverse problemspring\parameter estimate

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    9-015-UnearthingTruth-ModelingScenario
    This project introduces \textit{electrical resistivity tomography}, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical...

    Keywords: geophysicalImagingStatistical inverse problemtunnelconductionHolocaustVilniusDivergence TheoremfluxLaplace's equationimpedanceelectrical resistivity tomographytomographyresistivity

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    7-005-OverViewLaplaceTransforms-TechniqueNarrative
    This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.

    Keywords: integrationLaplace transformInverse Laplace transofrmintegration by parts

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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.

    Keywords: gravityinverse problemacceleration

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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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    Isolation and Functional Analysis of a Pancreatic Enzyme in an Introductory Student Lab
    Structure and function are correlated at all levels of biology. This topic is typically addressed early in an undergraduate class in general or molecular biology before students have gained much...

    Keywords: Protein StructureproteaseEnzymechemical bondscatalysissolubility

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    2008-Duran-Caginalp-Parameter optimization for differential equations in asset price forecasting
    The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days.

    Keywords: financeinverse problemnumerical nonlinear optimizationasset flowfinancial market dynamicsmarket return prediction algorithm

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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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    How Do Kidneys Make Urine From Blood? Qualitative and Quantitative Approaches to Filtration, Secretion, Reabsorption, and Excretion
    The function of the kidneys is to help maintain a constant internal environment (homeostasis) by regulating the volume and chemical composition of the blood. This regulation occurs via three...

    Keywords: collecting ductexcretionglomerular filtration rate (GFR)nephron tubulereabsorptionrenal corpusclesection

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    7-040-TankInterruptMixing-ModelingScenario
    We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

    Keywords: Laplace transforminverse Laplace Transformsalttankmixinginterrupt

    307

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