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    Modeling Scenario
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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.
    attritionLanchester modelpredator-predatorN-square Law
    Modeling Scenario
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    406

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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Modeling Scenario
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    287

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    3-011-EulerBallThrowing-ModelingScenario
    If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
    codingdragonVectorsEuler's methodball
    Modeling Scenario
    364

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    264

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    6-040-StruggleForExistence-ModelingScenario
    We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters
    competitionlogisticcarrying capacityparamecium
    Modeling Scenario
    444

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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 reactions.
    kineticschemistryLaw of Mass Actionchemical kineticsorder of reactionchemical reaction
    Modeling Scenario
    318

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    156

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    1-044-CollegeBound-ModelingScenario
    Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.
    interest ratecollege savingtuitionroom and board
    Potential Scenario
    121

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    70

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    2015-Goodnow-EtAl-Mathematical Models of Water Clocks
    This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.
    Torricelli's Lawwater clockBernoulli's Lawclepsydra
    Potential Scenario
    146

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    51

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    1991-JR_Lobry-P_Flandois-Comparison of Monod's Growth Model Parameters from the Same Data Set
    The paper obtains the parameters in Monod's Growth model using a minimization of the sum of square errors with a given data set and obtains confidence intervals
    Confidence intervalssum of square errorslinearizationgrowthModo Growth model
    Potential Scenario
    155

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    77

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    1992-John_Mathews-Bounded population growth-a curve fitting lesson
    The purpose of this article is to present two methods for fitting the logistic curve to data supplied by the U. S. census bureau.
    datalogisticlinearizationfitting
    Potential Scenario
    114

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    43

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    1994-S_S_Everingham-C_Peter_Rydell-Modeling the Demand for Cocaine
    This is a report prepared for the Office of National Drug Control Policy of the United States Army by the Rand Corporation. The report contains lots of data and builds a two compartment difference equation model.
    drugstwo compartmentcocainedemand
    Modeling Scenario
    1155

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    625

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    3-065-UpDown-ModelingScenario
    We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
    terminal velocityNewton's Second Law of Motionvelocitymotionapex
    Potential Scenario
    164

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    74

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    2014-Michael_Monagan-The Mortgage Payment Problem Approximating a Discrete Process with a Differential Equation
    In this article and a subsequent article I will give two non-standard examples that I've found helpful. The one presented here is a first order linear system. Second order systems and non-linear systems.
    compartmentheatinghouse
    Potential Scenario
    167

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    66

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    2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
    This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of Coolingbiochemical reactionsPoiseuille’s Lawstopping distance
    Modeling Scenario
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    280

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    1-145-FastPitch-ModelingScenario
    We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
    Measurementresistanceair resistancebaseballpitcherfast
    Modeling Scenario
    240

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    49

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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen M&M falling M up when tossed).
    Probabilitystochastic processesBayesian methodsprobability distribution
    Modeling Scenario
    343

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    278

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    3-017-StackedCoffeeFiltersFalling-ModelingScenario
    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.
    dataresistancefalling bodycoffee filterstacked
    Modeling Scenario
    210

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    239

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    4-036-AltitudeDependentGravity-ModelingScenario
    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
    agravityprojectilelinearizationltitufealtitude
    Modeling Scenario
    187

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    164

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    3-150-ItsABlastFurnace-ModelingScenario
    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
    steady stateheat equationinverse problemfurnace
    Potential Scenario
    143

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    43

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    2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
    The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.
    Fredholm integral equation ofLeontief’s modelmacroeconomic processes
    Potential Scenario
    146

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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