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    3-099-PullBack-ModelingScenario
    We guide students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own...

    Keywords: dynamicspull-back toy

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    3-061-ChemEngApps-ModelingScenario
    Students go through a chemical engineering problem: calculate concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation; then analyze the...

    Keywords: Spanishporous mediumcatalyisiscyclohexenehydrogeldehydrogenationhyperbolic trig functions

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    Quantitative biology: how educators that "buy-in" demonstrate greater productivity in teaching scholarship
    Poster presented at the University of Pittsburgh undergraduate research symposium on the impact of buy-in on productivity in faculty mentoring networks.

    Keywords: faculty mentoring networks

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    2006-Matt_MacWilliams-Developing ODEs to Describe the Motion of a Paper Helicopter
    This paper attempts to create a model that describes the motion of a paper helicopter using engineering, physical and statistical knowledge.

    Keywords: experimental designhelicopter

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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of...

    Keywords: resistanceprojectile motionprojectilefluidMersenne

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    1-092-DashItAll-ModelingSenario
    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting...

    Keywords: datarunningsprintHill-Kellerworld recordOlympics

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    1-105-AnimalFall-ModelingScenario
    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

    Keywords: animalNetwon's Second Law of Motionfalling bodyterminal velocityair resistanceNewtonair frictionfall

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    3-063-FallingBuildingIce-ModelingScenario
    We model the fall of a piece of ice which is falling from a high building in New York City.

    Keywords: resistancefallinggravityiceterminal velocityskyscrapers

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    2006-Han-EtAl-Ordinary differential equation models for ethanol pharmacokinetic based on anatomy and physiology
    Physiologically-based pharmacokinetic (PBPK) models have been used to describe the distribution and elimination characteristics of intravenous ethanol administration.

    Keywords: liverwortsintraveneouspharmacokineticsethanolethanol infustionpharmacodynamictissue model

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    3-052-OptimalProjectileFiring-ModelingScenario
    We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.

    Keywords: projectile motionprojectilelaunch anglemaximum range

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    3-033-S-TimeUpTimeDown-ModelingScenario
    We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.

    Keywords: projectile motionapexvertical motion

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    2002-Chai-Optimal initial angle to fire a projectile
    Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance...

    Keywords: optimizationprojectile motionlaunch angle

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    1994-T_Gruszka-A Balloon Experiment in the Classroom
    The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,

    Keywords: resistancefalling bodydragballoon

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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.

    Keywords: mathematical modelsystemmechanicalRomeo and Julietlovelove-hatejealousyShakespeare

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    1-050-BargingAhead-ModelingScenario
    As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.

    Keywords: optimizationkineticsenergytrophic efficiencyworkriverterminal velocityfrictioncurrentforcebargeworlkspeed

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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction....

    Keywords: population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts

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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?

    Keywords: projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance

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    2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
    After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological...

    Keywords: stochasticSIR modeldeterministicincubationinfectives

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    A Momentum-First Approach to Newton’s Second Law
    Students frequently struggle with seeing the connection between forces and motion in introductory physics. This lesson is part of a combined momentum and kinematics unit that first teaches...

    Keywords: group workMomentumNewton's Laws

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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...

    Keywords: Euler's methodTaylor's Methodsearch and rescueCoaast Guardlost at sealongitudelatitudelimit definition

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