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    Technique Narrative
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    7-005-OverViewLaplaceTransforms-TechniqueNarrative
    This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.
    integrationLaplace transformInverse Laplace transofrmintegration by parts
    Modeling Scenario
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    362

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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts
    Potential Scenario
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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
    Potential Scenario
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    1987-Claude-Marmasse-Studies on differential equations of enzyme kinetics-Biomolecular scheme
    The integral curve is compared with the solutions given by the two classical approximations to the problem: it is shown that the steady-state approximation is to be preferred to the rapid equilibrium theory as a general method.
    steady-state modelisoclinesenzyme kinetics
    Modeling Scenario
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    209

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    6-018-ExploringSIRModel-ModelingScenario
    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models.
    population dynamicssensitivitydiseaseSIR modelsepidemicrumors
    Modeling Scenario
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    206

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    3-071-WirelessTelegraphy-ModelingScenario
    This project has three parts, (1) done at home, (2) and (3) in class. In (1) we recall how to solve second order differential equations with constant coefficients and simple source functions. In class understand resonance and beats.
    bRLC circuitresonancebeatscurrentwireless telegraphyLC circuit
    Modeling Scenario
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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
    Modeling Scenario
    366

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    214

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    1-092-DashItAll-ModelingSenario
    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
    datarunningsprintHill-Kellerworld recordOlympics
    Modeling Scenario
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    3-034-CarSuspension-ModelingScenario
    We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
    designspring-mass-dashpotspring constantunderdampingcar suspensionsuspension tolerancestatic equilibrium
    Modeling Scenario
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    537

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    1-132-DigoxinElimination-ModelingScenario
    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    nullclinespharmacokineticsdigoxindrug eliminationtwo compartment
    Modeling Scenario
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    357

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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery
    Potential Scenario
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    2011-Nancy_Rodrıguez-Applied Partial Differential Equations in Crime Modeling and Biological Aggregation
    In the first part we study a fully-parabolic system of PDEs for residential burglary ‘hotspots’ (spatio-temporal areas of high density of crime). In this work we are concerned with the existence and uniqueness of solutions of this model. In
    biologyDiffusionKeller-Segel modelchemotaxiscrime
    Potential Scenario
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    46

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    2005-Minna_Wedenberg-Pharmacokinetic modeling of gastric emptying
    The development of new drug substances is a complex, time consuming and expensive process. Reducing the time for drug development and avoiding late termination of candidate drugs are important challenges for the pharmaceutical industry.
    paracetamolpharmacokineticsstomachsmall intestinesulfapyridine
    Free Online Textbook
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    2014-William_Trench-Elementary_Differential_Equations-Books_and_Monographs
    This is the most widely cited and referenced free online text for differential equations and is very complete. These two books are exactly what they say they are.
    differential equationstextbook
    Free Online Textbook
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    2017-Andrew_Lewis-Introduction_to_Differential_Equations_for_Smart_Kids
    The author addresses the question, "If I do not teach all of the usual techniques and tricks for solving differential equations, what do I replace it with?" in a number of wonderful ways.
    differential equationsmodelingtextbook
    Potential Scenario
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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
    cancertumorfittingagent-based
    Modeling Scenario
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    3-054-Relay-ModelingScenario
    We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.
    distanceprojectile motionrelaytimebaseballoutfieldhome plateminimization
    Modeling Scenario
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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
    Free Online Textbook
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    2015-H_Sayama-Intro to Modeling and Analysis of Complex Systems
    Introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science.
    textbooktext
    Modeling Scenario
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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
    optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth