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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and...

    Keywords: Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time

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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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    6-068-VisualizingPredator-PreyCycles
    In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be...

    Keywords: nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle

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    Preparing Student Study Guides through Peer Collaboration in the Technological Era
    Incorporating active learning exercises into large lecture courses is particularly challenging, especially when it comes to examination preparation materials. Traditionally, study guides are used...

    Keywords: active learningDiscussionStudy Skills

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    Two-Species Model
    These two Excel worksheets simulate the population growth of two interacting species. In isolation, each species grows logistically, but interaction effects between species may limit or enhance...

    Keywords: population growthcompetition modelsLotka-Volterra

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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.

    Keywords: phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation

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    A Lesson on Matter and Energy at the Organismal Scale: Linking Patterns and Processes Across Diverse Taxa
    Pathways and transformations of energy and matter (PTEM) are a conceptually challenging but essential component of biological literacy. Curricular gaps about PTEM nevertheless remain; although...

    Keywords: plantsenergyAnimalsfungimatterorganismal scale

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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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    2017-Guy-Bart_Stan-Modelling in Biology
    This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.

    Keywords: spring massbifurcationmass actionlimit cycles

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    Using Synthetic Biology and pClone Red for Authentic Research on Promoter Function: Introductory Biology (identifying new promoters)
    Students often memorize the definition of a transcriptional promoter but fail to fully understand the critical role promoters play in gene expression. This laboratory lesson allows students to...

    Keywords: bacteriasynthetic biologygene regulationtranscriptionstudent researchcentral dogmacloningpromoterreporter gene/protein

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    Using Online Materials/Videos to Enrich Linear Algebra for Scientists
    Part of the 2015 SMB Minisymposium: Topics in Biomathematics Education

    Keywords: courselinear algebrabiology majors

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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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    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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    Using Synthetic Biology and pClone Red for Authentic Research on Promoter Function: Genetics (analyzing mutant promoters)
    Students often memorize the definition of a transcriptional promoter but fail to fully understand the critical role promoters play in gene expression.  This laboratory lesson allows students...

    Keywords: bacteriasynthetic biologygene regulationtranscriptionstudent researchcentral dogmacloningpromoterreporter gene/protein

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    2017-Chávez-EtAl-Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations
    The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM).

    Keywords: bifurcationschaosimpulsive modellimit cycleshysteretic effectsperiod-doubling cascades

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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market...

    Keywords: Optimal Control Theoryadvertisingsales

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    1-054-GrowthInFarmland-ModelingScenario
    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model,...

    Keywords: fittingfarmfarmland

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    21st Century STEM Workforce Skills
    This activity includes a leadership assessment and associated exercise to encourage the development of 21st Century STEM Skills.

    Keywords: collaborationteam scienceleadership skills

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    Biobyte 1 - Where are we in the data science landscape?
    This short activity can be used to introduce the NAS Data Science For Undergraduates report's definition of data acumen and engage participants in a self assessment of how they connect with those...
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    A “Rule-of-Five” Framework for Models and Modeling
    In this paper, we extend the “Rule-of-Four,” initially used in calculus reform efforts, to a “Rule-of-Five” framework for models and modeling that is inclusive of varying disciplinary definitions...
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