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    Potential Scenario
    148

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
    goal functionabsolute error curvesinvers methodholling-Tanner model
    Modeling Scenario
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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
    Potential Scenario
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    2016-Erno_Keszei-Chemical Kinetics for Beginners
    The most important goal of kinetic research is the identification and characterisation of elementary molecular events which make possible the transformation of reactants into products.
    kineticszeroth order reactionfirst order reactionsecond order reactionreaction ratesthird order reaction
    Potential Scenario
    162

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    2013-Clarke-Skirba-Rationale and resources for teaching the mathematical modeling of athletic training and performance
    It is advisable that the professionals involved learn the various tools available for designing effective training programs.
    fitnessexercise physiologycritical power modelBanister impulse-response modelcoaching educationphysical fitnessperformance modeling
    Modeling Scenario
    348

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    542

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    1-082-MirroMirror-ModelingScenario
    This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical...
    astronomymirror climate change mitigation ocean deacidificationopticstelescopelensFoucaultinterpolation
    Potential Scenario
    121

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    38

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    2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
    Walk through the cases in context of second order linear constant coefficient differential equation with driving function
    driving functionviscousmechanical system
    Modeling Scenario
    391

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    265

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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 B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Potential Scenario
    248

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    38

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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium
    Potential Scenario
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    53

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    2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
    This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.
    sustainabilityfishFishingmanagementharvestfisherstrategyoverfishing
    Modeling Scenario
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    397

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    3-050-CometOrbitalMechanics-ModelingScenario
    The broad goal of this activity is to use a basic numerical method to approximate the solution of an initial value problem. In this particular case, we will use Euler's method to help model the trajectory of a comet as it orbits the sun.
    trajectorySpaceEuler's methodorbital mechanicscometorbit
    Potential Scenario
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    81

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    2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
    Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
    kinematicscurve designhighway exittangential acceleration
    Modeling Scenario
    643

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    545

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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
    Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo
    Modeling Scenario
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    213

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
    Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency
    Potential Scenario
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    2015-Joshi-EtAl-Optimal control of an SIR model with changing behavior through an education campaign
    We study stability analysis and use optimal control theory on the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost).
    SIR modelsvaccinepopulationwater treatmentsusceptibleeducation campaignminimizing costinfected
    Potential Scenario
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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
    Trigonometric Functionscirclesquigonometryinverse functiontrigonmetry
    Potential Scenario
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    2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
    We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
    Expected ValueRiemann sumnet change
    Potential Scenario
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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
    TrigonometryTrigonometric Functionsparametric equationscirclesinecosinesquigonometryinverse function
    Modeling Scenario
    292

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    133

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    1-089-SpreadOfDisease-ModelingScenario
    In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...
    SIR modelProportionderivativedifference quotientSleeping Beautycontagious disease
    Potential Scenario
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    2012-Nokkaew-EtAl-Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm
    This paper presents a double layer genetic algorithm (DLGA) to improve performance of the information-constrained parameter estimations.
    optimizationalgae growthgenetic algorithmssimulated dataconvergence of parameters
    Potential Scenario
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    2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system
    A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The
    glucose tolerance testsum of squared residualsmultiple shooting methodcost function