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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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    2015-Beier-EtAl-Building Context with Tumor Growth Modeling Projects in Differential Equations
    Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course...

    Keywords: tummor growthresearch experience

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    2014-Patel-Schlijper-Models of Consumer Behavior
    The problem posed to the Study Group was to construct models for consumer behaviour that might be useful in tools for brand management in markets for fast-moving consumer goods.

    Keywords: consumer behaviormarket share

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    2014-Michael_Monagan-The Mortgage Payment Problem Approximating a Discrete Process with a Differential Equation
    In this article and a subsequent article I will give two non-standard examples that I've found helpful. The one presented here is a first order linear system. Second order systems and non-linear...

    Keywords: compartmentheatinghouse

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    2013-Alicia_Caldwell-Students Rise to the Challenge of Modeling Yeast Growth Despite Sour Hiccups from Imperfect Data
    This paper describes a lab in which students in an Applied Mathematics in Biology course observe the growth of Saccharomyces cerevisiae, a yeast strain, in differing sugar concentrations for use in...

    Keywords: Saccharomyces cerevisiaelogisticyeastdeathgrowthsugaralcohol

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    2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
    We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.

    Keywords: experimental designsystems biologyAssociation & Data Fittingreaction ratesdecay rates

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    2012-Nokkaew-EtAl-Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm
    This paper presents a double layer genetic algorithm (DLGA) to improve performance of the information-constrained parameter estimations.

    Keywords: optimizationalgae growthgenetic algorithmssimulated dataconvergence of parameters

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    2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states
    We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states.

    Keywords: chemical engineeringsmoothing-based relaxation method

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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

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    2011-Nancy_Rodrıguez-Applied Partial Differential Equations in Crime Modeling and Biological Aggregation
    In the first part we study a fully-parabolic system of PDEs for residential burglary ‘hotspots’ (spatio-temporal areas of high density of crime). In this work we are concerned with the existence...

    Keywords: biologyDiffusionKeller-Segel modelchemotaxiscrime

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    2011-Mandal-EtAl-Mathematical models of malaria
    The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second is to...

    Keywords: epidemiologytransmissionhost-parasitemalariaRoss model

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    2010-Soetaert-EtAl-Solving Differential Equations in Rd SIMIODE Draft (5)
    Here we give a brief overview of differential equations that can now be solved by R.

    Keywords: solving

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    2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
    We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.

    Keywords: kineticschemical kineticszeroth order reactionfirst order reactionsecond order reaction

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    2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
    In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.

    Keywords: SASsuperpositionpharmacokineticscompartmental modelsmultiple dose

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    2009-Schaffer-Bronnikova-Controlling malaria
    The present paper reviews potential control strategies from the viewpoint of mathematical epidemiology.

    Keywords: epidemiologymalariabifurcationmosquitotransgenic mosquitoes

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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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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.

    Keywords: predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium

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    2008-Ratneesh_Suri-Optimal harvesting strategies for fisheries-differential equations approach
    We develop and investigate the harvesting model in both deterministic and stochastic settings. We first employ the Expected Net Present Value approach and determine optimal harvesting policy using...

    Keywords: optimal controlsustainable yieldmaximum sustainable yieldharvestExpected Net Present Valuecalculus of variationsdynamic programmingmaximum economic yield

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    2008-Fogler-etAl-Elements of Chemical Reaction Engineering  Strategies for Creative Problem Solving
    This is a website with lots of modeling information, exercises, and lessons.

    Keywords: chemical reaction

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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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