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    2016-Banks-EtAl-Modeling Bumble Bee Population Dynamics with Delay Differential Equations
    To provide a tool for projecting and testing sensitivity of growth of populations under contrasting and combined pressures, we propose a delay differential equation model that describes...

    Keywords: population modelReproductionspline approximationsBombus terrestrisneonicotinoidsbumble bee

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    2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
    Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without...

    Keywords: delayHIV-1T cellscombination antiviral therapy

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    9-020-HeatDiffusion-ModelingScenario
    This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular,...

    Keywords: laboratoryDiffusionheat

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    3-110-MilitarySpringMassApplication-ModelingScenario
    The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation,...

    Keywords: dampingresonancebeatsspring-mass systemLaplace TransfomDirac Delta function

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    4-060-CircuitTuner-ModelingScenario
    We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to...

    Keywords: resistanceciircuittuned mass tunerfrequencyKirchhoffvoltagegainfrequency responseamplitudes Voltage LawinductancecapacitorI am currently working in redesining an existing microbiology course. I would like to be part of ed

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    Fitting Exponential and Logistic Growth Models to Bacterial Cell Count Data
    In this activity, students will model a noisy set of bacterial cell count data using both exponential and logistic growth models. For each model the students will plot the data (or a linear...

    Keywords: modelingdata analysislinear regressiongraphingExponentsoptimizationcalculusInterpreting GraphsFunctionsqbccCellular and Molecular BiologyChoosing modelsUnderstanding ratesConcepts in Statisticsmeasurementsmanipulating equationscreating graphsExponential and Logarithmic Functionsinterpreting tables

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    2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
    In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.

    Keywords: Accelerometersfree falljumptrampoline

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    4-065-GasInjection-ModelingScenario
    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest...

    Keywords: Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN

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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.

    Keywords: gravityinverse problemacceleration

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    2018-Banerjee-EtAl-Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey
    The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of...

    Keywords: predator-preynonlocal consumptionTuring bifurcationspatial Hopf bifurcationspatio-temporal patternprey growth

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    2009-Reid-King-Pendulum Motion and Differential Equations
    This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect...

    Keywords: pendulumphysical pendulum

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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.

    Keywords: parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race

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    1999-F_Brauer-What_Goes_Up_Must_Come_Down
    It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces that are nonlinear...

    Keywords: resistancefallingprojectilevertical projectile

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    2017-Russell+Herman-A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers
    This is a self-published text book with excellent coverage and solid mathematics and theory to support applications.

    Keywords: textbookengineeringapplications

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    5-005-StiffDifferentialEquations-TechniqueNarrative
    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may...

    Keywords: Euler's methodexplicit methodsimplicit methodsstiffsitffnessstiff differential equationinstability

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    1-095-RatingChessPlayers-ModelingScenarios
    The goal of this activity is to have students build a mathematical model involving a system of first order difference equations from a verbal description of a scenario.

    Keywords: simulationchessElo's methodchess rating

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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is...

    Keywords: DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law

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    4-039-FallingDarts-ModelingScenario
    we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and...

    Keywords: optimizationresistanceterminal velocitymuzzle velocitydrag coefficientfree fallair drag

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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF)...

    Keywords: vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension

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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of...

    Keywords: optimizationsum of square errorsvector calculusLagrange multipliersline integrals

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