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    1994-Roland_Minton-A Progression of Projectiles-Examples from Sports
    There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,

    Keywords: sportsresistanceprojectilebaseballdraglinear resistancequadratic resistancetennis

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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.

    Keywords: differential equationsdifference equationfirst orderderivative definitionant tunnel

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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form...

    Keywords: computationerrorTorricelli's Lawdata fittinglinear approximation

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    The Importance of Street Trees and Urban Avifauna: A lesson exploring the relationship between urban forest and foraging birds
    This module examines the relationship between street trees, urban avifauna, and socioeconomic gradients in the highly urbanized county of Los Angeles, California. Using edited data from a published...

    Keywords: conservationBiodiversityurbanizationGeneralized linear modelsavifaunaurban forestsocioeconomicsstreet treesnegative binomial regression

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    The Influence of Exotic Plant Invasion on Pollinator Abundance
    This lesson introduces two global change factors, natural habitat loss and exotic plant invasion, and analyzes how these stressors impact the biodiversity and abundance of pollinator species....

    Keywords: statisticsinvasion biologyecologyRStudioBiodiversityInvasive SpeciesPearson correlation coefficientgeneral linear modelsinvasive plantspollinatorsPopulation abundance

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    1-109-EmployeeAttrition-ModelingScenario
    This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations.

    Keywords: populationlinear growthdecayemployeeattrition

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    Using Linear Regression to Explore Environmental Factors Affecting Vector-borne Diseases
    In this activity students will use linear regression to analyze real data on vector-borne diseases and explore how environmental factors such as climate change or population density influence the...

    Keywords: ecologygraphingmicrobiologyqbccUnderstanding ratesCreate graphsInterpret graphsinterpret tablesConcepts in Statistics

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    2016-Langtangen-Pedersen - Scaling of Differential Equations
    Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations...

    Keywords: scalingdimensionlesscontinuum mechanics

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    A Short Bone Biomechanics Primer: Background for a Lesson on Bone Viscoelasticity
    The skeletal system is the first of the body systems that we discuss in-depth in our Physiology & Anatomy courses (PNB 2264/2265 and PNB 2274/2275) in the Department of Physiology and...

    Keywords: structure-functionbiomechanicsAnisotropyViscoelasticity

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    2000-Erdman-Morelock-A Study of Kinetics The Estimation and Simulation of Systems of First-Order Differential Equations
    This paper introduces new and old features of the SAS System for the estimation and simulation of systems of first-order differential equations with emphasis on examples in kinetics.

    Keywords: kineticsSAScompartmentpharmacokinetics

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    BioNumbers-the database of key numbers in molecular and cell biology
    BioNumbers is a database of key numbers in molecular and cell biology—the quantitative properties of biological systems of interest to computational, systems and molecular cell biologists

    Keywords: dataResources @ BioNumbersNumbersestimationdatabaseResources @ QUBES - Teaching & Reference

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    2017-Helen-Byrne-Further Mathematics Biology
    These studies will be in the context of ecological, biological and biochemical applications.

    Keywords: epidemicschemotaxisenzyme-substrateion channelsnerve pulsesgene proagationtumour

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    2014-Chivers-EtAl-Predator-prey systems depend on a prey refuge
    We present an agent-based model which does not require the factors or constraints of previous models to reproduce all six patterns in persistent populations.

    Keywords: Individual & Agent Based Modelingpredator-preythink-pair-shareslynxrefugeprey switchingMustela-Clethrionomys systempatter oriented

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    1977-Michael_Mackey-Leon_Glass-Oscillation and Chaos in Physiological Control Systems
    First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle...

    Keywords: sensitivitychaosparametersRespirationdelayblood cells

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    Biometeorology of Asthma in South Florida: From Statistical Analysis to Mathematical Modeling
    Part of the 2015 SMB Minisymposium: Topics in Biomathematics Education

    Keywords: data analysisdynamical systemsmathematical modelingsynchronizationasthmaimmune systemcomplex systemsfeedback loopsself-organized criticalitychaos

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    How Luxury and Legacy Effects Shape Urban Avifauna in Los Angeles, California
    Is L.A.’s bird population shaped by historic redlining and income inequality? This lesson will introduce luxury and legacy effects hypotheses as they relate to urban avifauna in LA neighborhoods....

    Keywords: ANCOVASimple Linear Regressionurban ecologyredliningavian ecology

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.

    Keywords: spring massoscillationHooke's Lawcoupled springsperiodicforcing functionphase portrait

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    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.

    Keywords: random perturbationBrownian motionLangevin equationRiemann-Steiltjes integralWiener processIto's calculus

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    1-110-TidePoolSnails-ModelingScenario
    Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the...

    Keywords: datasnailstemperatureNewton's Law of CoolingcoolingNewtonwarmingtital pooltide pool

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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with...

    Keywords: datalogisticracismprejudicemisinformationmemesspreaddisinformationinformationliesGoogle Trendscoinspennies

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