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    Article or Presentation
    172

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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
    circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit
    Modeling Scenario
    442

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    263

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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
    transfer functionpolycarbonatebaby heatercoupled systemheating
    Modeling Scenario
    253

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    7-020-ThermometerInVaryingTempStream-ModelingScenario
    We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
    temperaturesteady statethermometerheat exchangetransfer functionphase lagInvers Laplace Transform
    Potential Scenario
    209

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    50

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    2004-Mitchell-von Meien-Krieger-Dalsenter-A review of recent developments in modeling of microbial growth kinetics
    Mathematical models are important tools for optimizing the design and operation of solid-state fermentation (SSF) bioreactors. Such models must describe the kinetics of microbial growth.
    Filamentous Fungisolid-state fermentationgrowth kineticsdiffusion-reactionoxygen transfer
    Article or Presentation
    184

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    53

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    0

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    2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
    optimizationdiscoveryFourierFourier seris
    Modeling Scenario
    430

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    261

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    0

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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 homogeneous while the other one is non-homogeneous.
    DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law
    Modeling Scenario
    398

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    176

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    7-008-MachineReplacement-ModelingScenario
    Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
    Probabilityreplacement numberLaplace transformindustrial engineeringmachineconvolutiondistributiojstep functionderivative definition
    Potential Scenario
    258

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    88

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    2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
    The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
    HangtimeTauberian IdentitiesRoad RunnerWile E. Coyote
    Potential Scenario
    156

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    61

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    1989-R_Blickhan-Spring Mass Model For Running-Hopping
    A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.
    spring massjumpjumping
    Potential Scenario
    170

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    38

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    1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
    A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
    plantoscillationdelaycircumnutationturning
    Technique Narrative
    757

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    222

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    0

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    7-006-LaplaceTransformBirth-TechniqueNarrative
    We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
    Transformationspower series
    Technique Narrative
    529

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    232

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    1-002-IntegratingFactor-TechniqueNarrative
    We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
    Integrating Factor
    Modeling Scenario
    220

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    225

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    1-063-ThreeHoleColumnOfWater-ModelingScenario
    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.
    fallingcolumn of waterTorricelli's Lawmultiple spigotsspigots
    Modeling Scenario
    294

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    321

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    1-088-RoomTemperature-ModelingScenario
    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
    environmentclimatetemperatureNewton's Law of Coolingcoolingperiodic function
    Modeling Scenario
    249

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    117

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    3-041-UpDown-ModelingScenario
    Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.
    gravityprojectile motionfalling bodymaximum heightftiming
    Modeling Scenario
    285

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    214

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    1-108-PoissonProcess-ModelingScenario
    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.
    Probabilitysstochastic processesPoisson processwaiting timearrival
    Potential Scenario
    146

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    92

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    2017-Alex_Honchar-Neural Networks For Solving Differential Equations
    In this post I want to show how I applied simple feed-forward NNs to different differential equations with increasing complexity: ODEs, second order ODEs, and, finally, PDEs.
    neural networksCybenko theoremdiffusion equationfluid dynamics
    Technique Narrative
    373

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    197

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    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
    random perturbationBrownian motionLangevin equationRiemann-Steiltjes integralWiener processIto's calculus
    Free Online Textbook
    216

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    55

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.
    differential equationsmodelingtextbook
    Article or Presentation
    165

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    56

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    1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom
    The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick.
    differential equationsresistancegravityfree fallaccelerationballoon