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    Article or Presentation
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    2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex
    We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their...
    exponential growthsolutionslinear systemsdecayconjecture
    Article or Presentation
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    2017-Brian_Winkel-Let_Us_Do_It_Using_Modeling_in_the_Classroom
    In this article the author, Brian Winkel, Director of SIMIODE, attempts to make the case for modeling in the differential equations classroom by giving both rationale and examples.
    differential equationsmodelingclassroom
    Article or Presentation
    510

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    2007-John_Jungck-Ten_Equations_that_Changed_Biology-Mathematics_in_Problem-Solving_Biology_Curricula The author
    These equations were selected upon the basis of wide-spread recognition of the value of the models.
    biologyequationsten equations
    Article or Presentation
    249

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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
    180

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    42

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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
    Article or Presentation
    188

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    2004-Mark_McCartney-Using_second-order_ordinary_differential_equations_to_model_traffic_flow
    A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted.
    differential equationstraffic flowvehicle followsecond order
    Article or Presentation
    248

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    2011-Brian_Winkel-Cross_coursing_in_mathematics-physical_modeling_in_differential_equations_crossing_to_discrete_dynamical_systems
    We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course.
    differential equationsmathematical modeldifference equationcross courseconvert
    Article or Presentation
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    2012-R_B_Ogunrinde-J_Sunday-On_some_models_based_on_second_order_differential_equations
    This paper presents some models based on second order differential equations. This is a very straightforward article with good explanations of modeling assumptions.
    combatcombat modelspecies interaction
    Article or Presentation
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    56

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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
    circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit
    Article or Presentation
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    66

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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.
    differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility
    Article or Presentation
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    60

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    2018-Vajravelu-Teaching Large DE Classes
    Practical problem solving in science and engineering programs require proficiency in mathematics. Improving student performance and retention in mathematics classes requires inventive approaches.
    differential equationsLarge classlarge classroom
    Article or Presentation
    169

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    2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution
    In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.
    ProbabilityMeanPoisson processbirth and death processinfinite number of differential equations
    Article or Presentation
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    704

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    2020-TeachingModule-CarSuspension
    The modeling activity on car suspensions assumes that students have grappled with second order linear homogeneous differential equations with constant coefficients.
    modulesuspensioncar suspensionsecond orderTeaching Module
    Article or Presentation
    129

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    1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change.
    datafirst orderparameterAIDS
    Article or Presentation
    254

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    69

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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
    Article or Presentation
    204

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    63

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    2013-Brian_Winkel-Browsing_Your_Way_to_Better_Teaching
    We describe the use of browsing and searching (in libraries, on-line, inside sources, at meetings, in abstracts, etc.) as a way to stimulate the teacher of undergraduate mathematics, specifically in differential equations.
    resourcesmodelingteachingbrowsesources
    Article or Presentation
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    SIMIODE Spring 2024 Webinars - WikiModel
    WikiModel is cloud-based application and requires no installation and is run via a web-browser to facilitate rapid implementation. Equations are typed in as they appear in a textbook. ODEs are automatically integrated via Runge-Kutta methods.
    modelingSoftwaretoolapplicationWikiModelmodeling cycle
    Article or Presentation
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    2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
    Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays.
    delayHIV-1T cellscombination antiviral therapy
    Article or Presentation
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    1994-Brian_Winkel-Ant_Tunnels_and_Calculus
    A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.
    differential equationsdifference equationfirst orderderivative definitionant tunnel
    Article or Presentation
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    2009-Brian_Winkel-Population_modelling_with_MandMs
    Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.
    simulationparameter estimationimmigrationdeathdifference equation