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    3-011-EulerBallThrowing-ModelingScenario
    If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will...

    Keywords: codingdragonVectorsEuler's methodball

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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the...

    Keywords: driversteady statesum of square errors

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

    Keywords: Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency

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    Functional trait-based restoration. Can hybrid restoration enhance invasion resistance and ecosystem services?
    A hybrid restoration experiment in Hilo, Hawaiʻi, in an area of high biocultural conservation value, that address the ecological and philosophical issues involved in conducting restoration with a...

    Keywords: Invasive SpeciesagroforestryHawaii CountyRestoration Ecologyplant functional traitstropical forest

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    1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom
    The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a...

    Keywords: differential equationsresistancegravityfree fallaccelerationballoon

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    2012-Augustus-Wali-Mathematical Modeling of Uganda Population Growth
    The purpose of this paper focuses on the application of logistic equation to model the population growth of Uganda using data from 1980 to 2010 (inclusive).

    Keywords: population growthlogistic growthDrug and Alcohol detoxificationcarrying capacityvital coefficients

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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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    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...

    Keywords: delayHIV-1T cellscombination antiviral therapy

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    2007-Exben_Friis-Jensen-Modeling and Simulation of Glucose-Insulin Metabolism
    In this thesis one of the models of diabetes, Bergman’s minimal model is described trough derivation and simulations.

    Keywords: Metabolisminsulin resistanceglucosePID controllerintolerance

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    1999-Meade-Struthers-Differential Equations in the New Millennium-The Parachute Problem
    The parachute problem will be used to illustrate several essential features of the improved courses. In particular, it will be seen that the traditional version of the parachute problem is not very...

    Keywords: resistancefree fallparachutejumpskydiving

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    3-042-CatapultLaunch-ModelingScenario
    We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to...

    Keywords: projectile motioncatapultuphilllaunch angle

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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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    3-102-SpringMassDamped-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.

    Keywords: frequencymassoscillationstiffnessspring constantspring\dampedSingle Degree of Freedom Systemcoefficient

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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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    Why does Blood Flow Change? Investigating the Math of Blood Flow Dynamics
    This collection of activities explores the relationship between blood flow, pressure, and the factors of resistance through graphs and modeling direct and inverse variation.

    Keywords: quant biographingRatiosmathassessmentcollege algebraundergraduate educationphysiologyAnatomyhuman biologyvariationCardiovascular physiologyAnatomy & Physiologylab activityOpenStaxqbccmanipulate equationsUnderstanding fractionsChoosing modelsUnderstanding ratesEstimating answersUse elementary functionsCreate graphsInterpret graphsRates and ProportionsSolving Equations and Inequalities

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    Taking the Hassle out of Hasselbalch
    Mention pH in a classroom and you can almost see the inner yawn on the faces of your students. The definition may even roll easily from their lips. However, despite multiple exposures to the...

    Keywords: pHdrug uptakeHenderson-Hasslbalch equationmedical applicationspKa

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    Effect of the Intestinal Protein Snakeskin on the Lifespan of Fruit Flies: A Kaplan-Meier Survival Analysissource Draft (1)
    In this activity, students perform the Kaplan-Meier survival analysis on raw data obtained from an experiment that explores the effect of overexpressing the Snakeskin (Ssk) protein on the lifespan...

    Keywords: graphingBiochemistryhypothesis testingcalculus and biologyapproximating areas under curvesqbccCellular and Molecular BiologyCreate graphsInterpret graphsSolving Equations and Inequalitiesinterpret tablesConcepts in Statisticsusing statisticschi-square analysissurvival analysis

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    Evaluating the potential for immune escape: how likely is an antibody to protect against a specific SARS-CoV-2 variant?
    Commercial antibodies to the SARS-CoV-2 spike protein have been successfully used to treat people with COVID-19. Unfortunately, as the SARS-CoV-2 virus evolves, new variants have appeared that can...

    Keywords: course based undergraduate research experiencesBLASTmolecular modelingSARS-CoV-2antibodyNextstrainiCn3DSequence alignmentStructure alignment

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    Fly Exercise: A Simple Experiment to Test the Physiological Effects of Exercise on a Model Organism
    Model organisms are commonly used to study and experimentally explore biological processes in ways that are technically or ethically not possible in humans. For this reason, model organisms are an...

    Keywords: exerciseenzyme kineticsmetabolite concentrationmodel speciesphysical activity

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    5-040-TunedMassDamper-Part-I-Modeling Scenario
    We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original...

    Keywords: structurespring-mass-dashpotspring massearthquakevibrationtuned mass tunerrestoring forcecontroldampe

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