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    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our...

    Keywords: concentrationSurface AreacolorNewton's Law of Coolingteasugar

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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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    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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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.

    Keywords: Polynomial dynamical systembeamcantilever

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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a...

    Keywords: pendulumLotka Volterra equationsexistenceuniqueness

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    2012-Tweedle-Smith-Mathematical model of Bieber Fever-The most infectious disease of our time
    We develop a mathematical model to describe the spread of Bieber Fever, whereby individuals can be susceptible, Bieber-infected or bored of Bieber.

    Keywords: infectious diseasediseaseinfectionmediaJustin BieberBieber feversymptomsboredreproductive ratio

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    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.

    Keywords: exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano

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    1-044-CollegeBound-ModelingScenario
    Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.

    Keywords: interest ratecollege savingtuitionroom and board

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    1-047-Condensation-ModelingScenario
    We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and...

    Keywords: simulationsum of square errorscondensationbest fit

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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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    1-084-GoingViral-ModelingScenario
    Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of...

    Keywords: simulationlogisticrandomfittingpartial fractions

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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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    4-023-MysteryCircuit-ModelingScenario
    Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a...

    Keywords: filterscircuitRLC circuitKirchhoffvoltagegaindriver

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    Examining human impacts on tusk evolution in elephants using authentic research data
    In this activity students explore and analyze real, authentic research data paired with HHMI’s “Selection for Tuskless Elephants” video in a hands-on investigation of human impacts on elephant...
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    Modeling Strep Throat Detection, Infection, and Spread Using an SIR Model and the Vensim Simulation Software
    The overarching goal of this lesson is to provide students with an opportunity to gain experience making and using biological models. Biological modeling can be used to investigate complex,...

    Keywords: infectious diseasebiological modelingSIR model

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    Snapshot Serengeti: Implementing an online module about Serengeti wildlife ecology in a community-college ecology course
    This resource describes the implementation plan for an undergraduate ecology course at Muscatine Community College, Iowa, of an online module featuring a database on Serengeti wildlife populations....

    Keywords: ecologywildlifewildlife managementWildlife ecology

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    2009-James_May-Nonlinear vibration control of long flexible structures
    An automated, non-linear control scheme was developed to transfer energy from the fundamental vibration mode, where most vibration energy of the structures of interest resides, to higher order...

    Keywords: vibrationdampingtuned mass damperviscousnodalmodel dampingflexible structureenergy transfer

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    1999-Meade-Struthers-Differential Equations in the New Millennium-The Parachute Problem
    The parachute problem will be used to illustrate several essential features of the improved courses. In particular, it will be seen that the traditional version of the parachute problem is not very...

    Keywords: resistancefree fallparachutejumpskydiving

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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the...

    Keywords: population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery

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    3-001-SpringMassDataAnalysis-ModelingScenario
    We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass...

    Keywords: datadampingspring-mass systemNewton's Second Law of Motionspring constantHooke's Law

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