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    Modeling Scenario
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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
    evaporationconealcoholPetri dish
    Potential Scenario
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    35

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    2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics
    Step by step formation of drug absorption models is shown with many good graphics of system and plots. Solutions are offered but no solution methods are shown.
    Michaelis-MentenEnzymesubstratecompartmentpharmacokineticsrate constanturinary dataabsorption rate
    Potential Scenario
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    1975-David_Burghes-Population dynamics An introduction to differential equations
    In this paper a number of population models, which lead to differential equations, are derived. First-order variables separable equations are formulated from the Malthusian population model and its extension to include crowding effects.
    fishpredator-preylogisticpopulationdelaylag
    Free Online Textbook
    181

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    48

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    2017-Andrew_Lewis-Introduction_to_Differential_Equations_for_Smart_Kids
    The author addresses the question, "If I do not teach all of the usual techniques and tricks for solving differential equations, what do I replace it with?" in a number of wonderful ways.
    differential equationsmodelingtextbook
    Potential Scenario
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    37

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    2012-Gilbert_Koch-Modeling of Pharmacokinetic and Pharmacodynamics of Cancer and Arthritis
    In this work we develop preclinical PKPD models based on fundamental biological and pharmacological principles. Equipped with a PKPD model, different dosing schedules could be simulated.
    cancerpharmacodynamicsPKPD modelarthritisPharmacokineticanticancer
    Potential Scenario
    124

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    36

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Potential Scenario
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    90

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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.
    Algorithminverse probleminverse
    Technique Narrative
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    429

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    1-005-NavigatingNumericalMethods-TechniqueNarrative
    This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor...
    Euler's methodTaylor's Methodsearch and rescueCoaast Guardlost at sealongitudelatitudelimit definition
    Modeling Scenario
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    181

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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
    optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable
    Potential Scenario
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    65

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    2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
    In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.
    Accelerometersfree falljumptrampoline
    Potential Scenario
    154

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    45

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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 elaborate, using some of the representative mathematical...
    epidemiologytransmissionhost-parasitemalariaRoss model
    Potential Scenario
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    47

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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 various optimization techniques including optimal...
    optimal controlsustainable yieldmaximum sustainable yieldharvestExpected Net Present Valuecalculus of variationsdynamic programmingmaximum economic yield
    Potential Scenario
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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.
    sociologyarms racesaccumulative advantagealcoholismPeter Principlefemale mortalitypopulation pressureoccupational mobilitysocial mobilityRichardson theory of war
    Potential Scenario
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    1976-JG-Wagner-Computers in pharmacokinetics
    This is a seminal paper in pharmacokinetics in which the author introduces historic notions and approaches. As can be seen from the abstract there is a variety of material here.
    kineticscomputerparametersPharmacologydrugspharmacokinetics
    Article or Presentation
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    51

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    2011-Lorelei_Koss-Sustainability_in_a_differential_equations_course_case_study_of_Easter_Island
    Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in an ordinary differential course.
    differential equationssustainabilitypopulationEaster Islandcollapseenvironmental collapse
    Potential Scenario
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    37

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    2019-Banuelos_Danet_Flores_Ramos-Epidemiological_Math_Model_Approach_To_Political_System_with_Three_Parties
    A nonlinear compartmental model is derived to study the movement between classes of voters with the assumption of a constant population that is homogeneously mixed.
    politicsparametersvotingcompartment modelepidemiological modelequilibriathree-party system
    Modeling Scenario
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    1-001-MM-DeathAndImmigration-ModelingScenario
    We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!
    simulationimmigrationdeathSpanishdatsWinkelBrian Winkel
    Modeling Scenario
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    1-038-Ebola-ModelingScenario
    Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
    population dynamicsdata analysisexponential growthEbolalogisticepidemic
    Modeling Scenario
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    2010

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    3-030-SecondOrderIntro-ModelingScenario
    We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
    parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight
    Modeling Scenario
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    340

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    9-020-HeatDiffusion-ModelingScenario
    This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
    laboratoryDiffusionheat