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    2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.

    Keywords: optimizationdiscoveryFourierFourier seris

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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring...

    Keywords: energymass-spring systemkinetic energypotential energytotal energy

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    Exploring Random Mutation and Selection: Avida-Ed Lab Book Exercise 2
    An introductory activity exploring the role of random mutation in natural selection using the Avida-ED simulation.

    Keywords: avida-edmutationsoftware simulationsSelectionvariation

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    Diversity Indices: Simpson's D and E
    This module introduces Simpson's diversity index in the context of understanding how to mathematically measure the species diversity in a community. It is intended for an introductory biology...

    Keywords: ecologydiversityFunctionsOpenStaxdiversity index

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    Sizes of Organisms: The Surface Area to Volume Ratio
    This module introduces surface area-volume ratio in the context of understanding the limits or constraints on organism size. It is intended for an introductory biology audience.

    Keywords: RatiosstructureSurface AreabiomechanicsGeometryFunctionsVolumeOpenStax

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    Design a Zoo (Grades 3-5)
    This classroom lesson presents students with the job of designing a zoo, which could include modeling tasks ranging from choosing and locating the exhibits to setting the right admission prices.

    Keywords: unit costbudgetsdistance

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    Natural Selection and Galápagos Finches
    A worksheet and accompanying data set that guides students through making and interpreting frequency distributions, selection differentials, and fitness functions.

    Keywords: EvolutionResources @ HHMI - BioInteractive

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    4-036-AltitudeDependentGravity-ModelingScenario
    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order...

    Keywords: agravityprojectilelinearizationltitufealtitude

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    Computational Biology using R
    This is an introductory level course on computational biology.

    Keywords: simulationmoduleRcourseprojectsolutions

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    Geoscience Methods and Resources for K-5 Pre-Education Majors
    : Exploring Geoscience Methods was an excellent capstone experience for Elementary Education Majors. The class I used this module with was 24 students of various backgrounds and academic...

    Keywords: geneticsvideosQUBESecologyResources @ HHMI - BioInteractiveMathematical Biologycalculusjavaorganismal biologyquantitative biologybioinformaticsneurosciencegenomicscancerSecondaryyoutubemicrobiomeFaculty Mentoring NetworksalamanderCapture mark-recaptureAudience level - Introductory UG - majorsAudience level - Introductory UG - non-majorsecosystemsgenetic basis of diseasebiology of cellshuman reproductionfood chainIntroduction to Modelingrandom number generatorPost-secondaryLower DivisionPossible TasksModeling ProjectBuildCompareEvaluateexponential decayrecursionabsorptionelimination

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    1-002-IntegratingFactor-TechniqueNarrative
    We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to...

    Keywords: Integrating Factor

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    1-039-StochasticPopModels-ModelingScenario
    We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is...

    Keywords: Probabilitypopulation dynamicsVarianceMeanstochasticdeterministic

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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.

    Keywords: circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit

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    Waking up Anna - Adaptations and Conversion to Mol*
    This case focuses on understanding the molecular basis of Anna's sleeping disorder and its treatment. The adaptations addressed question clarity and reformatting to use Mol*.

    Keywords: sleepmolecular visualization and analysisPDBMolecular Case StudyGABAMolCaseNetMol*MolStarProtein visualizationFlumazenil

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    2021-G_Nagy-Ordinary_Differential_Equations
    This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and...

    Keywords: differential equationstextbook

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    1-001s-StochasticMDeathImmigration-ModelingScenario
    We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

    Keywords: simulationdatalogisticimmigrationstochasticdeathfitting

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    Waking up Anna
    This case focuses on understanding the molecular basis of Anna's sleeping disorder and its treatment.

    Keywords: sleepmolecular visualization and analysisPDBMolecular Case StudyGABA

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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number...

    Keywords: optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable

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    Happy Blue Baby
    This case, about a specific mutant of hemoglobin, focuses on visualizing and understanding the molecular basis of why an infant turned blue soon after birth and how the cyanosis resolved on its own...

    Keywords: mutationHemoglobinmolecular visualization and analysisgenetic basisPDBMolecular Case StudyMol*

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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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