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    Modeling Scenario
    242

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    1-067-ModelingWithSigmoidCurves-ModelingScenario
    The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.
    logisticGompertzsigmoidVerhulst-Pearl
    Potential Scenario
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    40

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor
    Modeling Scenario
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    1-126-MarriageMath-ModelingScenario
    We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along with two governing assumptions;.
    marriageGompertz function
    Modeling Scenario
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    266

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    1-081-TumorGrowth-ModelingScenario
    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth.
    logisticpopulationtumorGompertz
    Modeling Scenario
    253

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    218

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    1-066-USCensusModeling-ModelingScenario
    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.
    datalogisticpopulationGompertzcensusgoodness of fit
    Potential Scenario
    129

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    55

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    2001-Tsoularis-Analysis of logistic growth models
    variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. We further review and compare several such models.
    logisticGompertzVerhulstPearl and ReedBertalanffy
    Modeling Scenario
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    398

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
    optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy
    Modeling Scenario
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    272

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
    optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz
    Modeling Scenario
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    1-100-EngineeringDemographics-ModelingScenario
    Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women in the United...
    logisticpopulationImproved Euler MethodGompertzdemographicswomenautonomous
    Potential Scenario
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    39

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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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    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
    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
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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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    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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    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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    52

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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
    150

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    33

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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