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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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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model...

    Keywords: zombiesSIR modelsGame

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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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    2014-Michael_Monagan-The Mortgage Payment Problem Approximating a Discrete Process with a Differential Equation
    In this article and a subsequent article I will give two non-standard examples that I've found helpful. The one presented here is a first order linear system. Second order systems and non-linear...

    Keywords: compartmentheatinghouse

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    Riverbird distributions and habitat use
    Riverbirds are widespread, use diverse riparian habitats, and respond rapidly to changing conditions. Students can apply riverbird data to evaluate hypotheses about these responses, while gaining...

    Keywords: logistic regressionHabitat selectionRiver Field Studies NetworkWaterfowl raptorkingfisherheronfocal speciesmonitorriverbank

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    The Stomata Lab. What the past can tell us about our future - using fossil and modern plants to model atmospheric carbon dioxide
    Students will develop a mathematical model of the relationship between atmospheric CO2 and the number of stomata on a leaf (Stomata Index). They will evaluate the model graphically, statistically,...

    Keywords: introductory biologyQuantitative reasoninginterdisciplinaryclimate changeregressionEcology and EvolutionStomataNIQBC2. Data and GraphsC4. mathematical modelsC3. Statistical AnalysisSmithsonian

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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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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.

    Keywords: attritionLanchester modelpredator-predatorN-square Law

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    “Leveling Up” In Your Favorite Video Game Math Modeling Activity
    Students write linear equations that represent their model for solving a problem about playing video games.

    Keywords: modelingNIMBioslinear equationsmiddle grades (4-9)Middle SchoolSystems of Equations

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    Graphing bacterial growth rates: semi-log graphs v linear graphs
    In this activity, students will explore the concept of binary fission, generation time, and bacterial growth curves, with an emphasis on the log phase. Students will use semi-log graphs and linear...

    Keywords: graphingexponential growthMicrobiology Educationmicrobiologybacteriagrowth rateUndergraduate STEM educationCommunity College Educationqbccmanipulate equationsCellular and Molecular BiologyCreate graphsInterpret graphsbinary fissionsemi-log graphlinear graphgrowth curvecreating graphsExponential and Logarithmic Functions

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    THE IMPORTANCE OF GREEN SPACES & NATIVE PLANTS TO URBAN AVIFAUNA: A Lesson on how urban residential yards can support birds during their annual cycle
    In this lesson students will learn about the impacts of urbanization, and the conservation challenges it poses to wildlife, in particular avifauna. Introductory ecology topics such as the theory of...

    Keywords: birdsurbanizationPoisson Distributionnative plantsGeneralized linear models

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    A Potential Novel Ecosystem Service: Seagrass Meadows Reduce Disease in Nearby Corals
    In this lesson, students will receive an introduction to Poisson Generalized Linear Mixed Models in R utilizing data on coral diseases. In their code, students will assess if seagrass status has an...

    Keywords: environmental scienceseagrassecosystemcoral reefsEcosystem Services

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    1-104A-T-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions and comparing to actual...

    Keywords: regressioninfectionCOVID19carrying capacitylogistic equationexponential model

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    1-033-SouthernBarbeque-ModelingScenario
    We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the...

    Keywords: nonlinear regressionlogisticNewton's Law of Cooling-Warmingbarbecue

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    Avian Censys Analysis
    This Swirl course uses ecological data of bird counts and habitat variables to estimate inter-observer variability and the relationship of birds with habitat variables.

    Keywords: ecologyregressionaverageserror estimates

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    Islands as a Tool for Teaching Ecology and Evolution
    Module for Ecology & Evolution course covering island biogeography principles, The scientific process and hypothesis testing, statistical methods (t-tests, regression), and online database use...

    Keywords: moduleResources @ AIM-UP!species richnessBiodiversityIsland biogeographyAIM-UP

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