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    3-016-FallingCoffeeFilters-ModelingScenario
    We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.

    Keywords: resistanceFree Body Diagramcoffee filterforcegraviityfalling object

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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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    4-055-ShatterWineGlass-ModelingScenario
    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?

    Keywords: frequencydampingamplituderesonanceoscillationshatteringwine glassbridgesaircraftexternal force

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    Restoring tropical forests: Is planting clusters of trees a cost-effective and ecologically-sound strategy to restore tropical forest?
    This module (available in four languages) provides a broad introduction to both ecological and social aspects of tropical forest restoration. It focuses on a long-term study comparing three...

    Keywords: Restoration Ecologyforest restorationtropical forest

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    Restoring Tropical Forests: Implementing a module in an undergraduate majors’ course in forest ecology in Costa Rica
    This publication describes implementation of a module on tropical forest restoration in Costa Rica for an upper-level undergraduate course in forest ecology at the Instituto Tecnológico de Costa...

    Keywords: forest ecologyRestorationfield course

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    How We Help: Human elements of restoration ecology
    In this lesson, students recall the basics of restoration ecology, interpret and predict several graphs that explain restoration manager characteristics, and reflect on an interview with...

    Keywords: graph interpretationEcosystem Ecologyfmnconservation biologydata literacyinvasive plantsLGBTQRestoration Ecologyriparian ecologyNatural Resource ManagementBioGraphIrepresentation in STEM

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    2002-Dietz-Heesterbeek-Daniel Bernoulli-epidemiological model revisited
    The seminal paper by Daniel Bernoulli published in 1766 is put into a new perspective. After a short account of smallpox inoculation and of Bernoulli’s life, the motivation for that paper and its...

    Keywords: life tableepidemicsmallpoxDaniel Bernoullicompeting riskinoculation

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    1-057-FiguringFluidFlow-ModelingScenario
    We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which...

    Keywords: dischargetankTorricelli's LawConservation of Energyfluid flowheightliquid

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    2011-Therese-Keane-Combat modelling with partial differential equations
    We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.

    Keywords: Lanchester modeltroop dynamicsswarming behaviortroop regroupinglossesnon-local termslocal terms

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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier...

    Keywords: frequencyresonancecoupled oscillator

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    1999-Long-Weiss-The Velocity Dependence of Aerodynamic Drag A Primer for Mathematicians
    This paper is exactly what it says it is, namely, a Primer for Mathematicians. There are ample models, data, attention to such issues as Reynolds’ numbers, and attention to aerodynamics issues.

    Keywords: drag forceaerodynamics

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    1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
    The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which...

    Keywords: kineticsfirst orderreactionsecond orderzeroth order

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    3-065-UpDown-ModelingScenario
    We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and...

    Keywords: terminal velocityNewton's Second Law of Motionvelocitymotionapex

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    3-013-WhiffleBallFall-ModelingScenario
    We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.

    Keywords: Akaike Information CriterionresistancegravityFree Body Diagramforcefalling objectWhiffle ball

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    6-016-PandemicModeling-ModelingScenario
    The recent coronavirus outbreak has infected millions of people worldwide and spread to over 200 countries. How can we use differential equations to study the spread of coronavirus?

    Keywords: population dynamicsinfectious diseasediseaseEbolaeSIR modelsCOVID19pandemicepidemicreproduction number

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    Muscle Contraction
    This module introduces equations around muscle force in the context of understanding the Sliding Filament Model. It is intended for an introductory biology audience.

    Keywords: plottinghyperbolic equationsOpenStaxAnimal Physiology

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    Science Behind the Lesson: It's a Bird! It's a Plane! It's Biomechanics!
    Active flight is a specialized mode of movement found in insects, birds, and mammals. The anatomy, morphology, physiology, and ecology of flying taxa has changed over evolutionary time. Researchers...

    Keywords: EvolutionecologybatphysiologyAnatomybiomechanicsbirdFlightinsect

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    Invasion, Restoration, and Response: Assessing changes in arthropod community assemblage using both parametric and non-parametric approaches
    This lesson, which is based around a recently published paper in the Journal of Ecological Applications, introduces students to both parametric and non-parametric approaches to statistical analysis...

    Keywords: ecologyANOVAInvasive Speciesspecies diversityquantitative analysisupper level wetland ecologysalt marshesarthropodsShannon diversity indexleast significant differences

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    The River Field Studies Network: Connecting rivers, people, & science through immersive field-based education (RCN-UBE Introduction)
    Connecting rivers, people, & science through immersive field-based education

    Keywords: RCN-UBE Introduction

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    Prairie Eco Services (Project EDDIE)
    As densely populated urban areas continue to expand, human activity is removing much-needed greenspaces from our communities; in turn, we are also removing critical buffers that are needed to...

    Keywords: Project EDDIEWater cycle

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