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    Potential Scenario
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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.
    parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race
    Modeling Scenario
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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Potential Scenario
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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 satisfy trig like identities.
    Trigonometric Functionscirclesquigonometryinverse functiontrigonmetry
    Potential Scenario
    107

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    35

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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.
    Laplace transforminverse problemtankmixinginverse
    Potential Scenario
    100

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    2006-Chaachoua-Saglam-Modelling by differential equations
    This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations.
    historyseventeenth century
    Potential Scenario
    104

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    43

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    2019_Isaac_Eshakoff-Differential_Equations_of_Love_and_Love_of_Differential_Equations
    In this paper, simple ordinary differential equations are discussed against the background of William Shakespeare’s Romeo and Juliet.
    mathematical modelsystemmechanicalRomeo and Julietlovelove-hatejealousyShakespeare
    Potential Scenario
    176

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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
    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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    59

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    2017-Alex_Honchar-Neural Networks For Solving Differential Equations
    In this post I want to show how I applied simple feed-forward NNs to different differential equations with increasing complexity: ODEs, second order ODEs, and, finally, PDEs.
    neural networksCybenko theoremdiffusion equationfluid dynamics
    Potential Scenario
    120

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    39

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    1994-JM_McDill-Bjorn_Felsager-The Lighter Side of Differential Equations
    Although differential equations have many serious applications to the modeling of real-world problems, a few lighthearted problems can serve to motivate students and brighten their attitudes toward a computer-oriented course in differential...
    cooperationharvestingRomeo and Julietlovecannibalismovercrowding
    Potential Scenario
    166

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    86

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    2018-LA_Peletier-Ordinary Differential Equations in Pharmacodynamics
    Good mix of theory, application, solution technique in a number of areas of applications of differential equations. Develops qualitative behavior issues. Exercises, but not about models, more about the mathematics only.
    compartment modelpharmacokineticspharmacodynamicsorbitsturnover
    Potential Scenario
    105

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    42

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    2016-Pennell-Avitabile-White-Engineering Applications Differential Equations
    General discussion of an engineering based differential equations course with examples from RC Circuit, mass spring dashpot.
    circuitvoltagecapacitornondimensionalization
    Potential Scenario
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    85

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    2015-Jonathon_Easton, Jonathan-Mathematical models of health focusing on diabetes-Delay differential equations and data mining
    This is an exhaustive study with very good references of a linear system of four differential equations with and without delay to model diabetes in a human being.
    diabeteshealth model
    Potential Scenario
    104

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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 content via a writing or research experience.
    tummor growthresearch experience
    Potential Scenario
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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 performance for common access patterns.
    discretecachecache calculus
    Potential Scenario
    78

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    33

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    2011-Therese-Keane-Combat modelling with partial differential equations
    We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.
    Lanchester modeltroop dynamicsswarming behaviortroop regroupinglossesnon-local termslocal terms
    Potential Scenario
    111

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    31

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    1999-Marchand-McDevitt-Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations
    The project takes full advantage of analytical, numerical, and qualitative techniques to explore the mechanical vibrations of buildings during an earthquake.
    earthquakenondimensionalizationCoulomb dampingmechanical vibration
    Article or Presentation
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    2015-Differential_Equations-CUPM_Curriculum_Guide_to_Majors_in_the_Mathematical _Sciences
    This is a report from the working group charged with making recommendations for the undergraduate curriculum in differential equations.
    differential equationscurriculumCUPM
    Article or Presentation
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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
    vibrationresonancetuned mass damperpeak frequency responseexcitation
    Modeling Scenario
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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
    slope fieldspopulation