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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and...

    Keywords: Lanchester's lawssensitivity analysisanalysis

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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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    1-014-DrainingContainers
    Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the...

    Keywords: containerstankflowTorricelli's Lawdrainingfixed volume

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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.

    Keywords: projectile motionaccelerationNewton's Law of Coolingspeeding

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    2017-Zhang-Wang-Study on public opinion propagation in self media age based on time delay differential model
    We establish the Logistic equation, introduce the operator time delay differential equation, and finally establish the improved delay differential equation, which can describe the propagation trend...

    Keywords: propagationpubic opinionNetwork public opinionpropagation lawself-mediaXiongan New Area

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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight...

    Keywords: resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket

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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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    3-095-ShotInWater-ModelingScenario
    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.

    Keywords: projectile motionterminal velocityprojectilewater resistancereduction of orderfrictionair resistance

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    1-105-AnimalFall-ModelingScenario
    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

    Keywords: animalNetwon's Second Law of Motionfalling bodyterminal velocityair resistanceNewtonair frictionfall

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    1979-Brian_Winkel-Elementary_My_Dear_Watson_Differential_Equation
    Sherlock Homes explains to Doctor Watson how he solves a murdermystery using Newton's Law of Cooling.

    Keywords: Newton's Law of CoolingSherlock Holmestime of detah

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    9-002-GroundWaterFlow-ModelingScenario
    The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.

    Keywords: sgroundwater flowDarcy's Lawheat equationaquiferhydraulic headFourier's Lawsand tank

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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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    1-094-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

    224

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    1-140-LeakyBucket-ModelingScenario
    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top...

    Keywords: flowTorricelli's Lawleaky bucket

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    3-020-ChordPathTime-ModelingScenario
    Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is...

    Keywords: Unit CirclepathfallinggravitychordNetwon's Second Law of Motion

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    1-076-ClimateBifurcation-ModelingScenario
    We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.

    Keywords: energy balanceclimateenergyalbedoHysteresisbifurcationice-agegreenhousebalanceStefan Boltzmann Law

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    1-011-Kinetics-ModelingScenario
    We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order...

    Keywords: kineticschemistryLaw of Mass Actionchemical kineticsorder of reactionchemical reaction

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    A Momentum-First Approach to Newton’s Second Law
    Students frequently struggle with seeing the connection between forces and motion in introductory physics. This lesson is part of a combined momentum and kinematics unit that first teaches...

    Keywords: group workMomentumNewton's Laws

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    1-096-OP-AMP-Differentiator-ModelingScenario
    The output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and compared with...

    Keywords: simulationMeasurementfeedbackMultisimcircuitvoltageoperational amplifiervalidationSPICE

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    Electrical Activity of Neurons
    This tutorial describes how neurons generate action potentials, and how scientists measure neuronal activity and record the firing of individual neurons.

    Keywords: Resources @ HHMI - BioInteractiveAnatomy & PhysiologyNervous systemCell communication

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