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    Technique Narrative
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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
    computationerrorTorricelli's Lawdata fittinglinear approximation
    Potential Scenario
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    2017-Ben_Finio-Science Buddies – Linear & Nonlinear Springs Tutorial
    This tutorial provides a basic summary of linear and nonlinear springs and their associated equations for force, stiffness, and potential energy.
    spring massstiffnessspringspotential energyforcenonlinear springlinear spring
    Potential Scenario
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    2016-Roberto_Camporesi-A fresh look at linear ordinary differential equations with constant coefficients
    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator.
    impulseGreen functionsinstructional exposition
    Free Online Textbook
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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
    spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions
    Technique Narrative
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    1-060-RegularPerturbation-TechniqueNarrative
    This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
    perturbationregular perturbationasymptotic expansionsanalytical approximationBernoulli equation
    Technique Narrative
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    216

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    5-030-LinNonHomoSystemSol-TechniqueNarrative
    We offer strategies for solving linear systems of nonhomogeneous differential equations using a conjectured solution strategy for a system of constant coefficient, linear, n
    strategiesdiscovery learningeigenvectorseigenvalue
    Free Online Textbook
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    2016-Simon_Malham-Differential_Equations_and_Linear_Algebra
    This is a nice set of notes on which a course can be based. There is ample material on first and second order, linear systems, and Laplace Transform methods for setting up and solving differential equations.
    textbooklinear algebraLaplace transform
    Article or Presentation
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    2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling
    This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues.
    modulelinear systemsdigoxinTeaching Module
    Potential Scenario
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    1986-Cook-Witten-One-dimensional linear and logistic harvesting models
    Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed.
    logisticcontinuouspopulationlineardiscreteharvestinbg
    Technique Narrative
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    5-012-LinearSystemConjecture-TechniqueNarrative
    Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
    discovery learningconjecturesolutionsubstitution
    Potential Scenario
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    2003-Rasmussen-Keynes-Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations
    The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant...
    instructional designeigenvalueseigenvalue analysis
    Free Online Textbook
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    2021-G_Nagy-Ordinary_Differential_Equations
    This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations.
    differential equationstextbook
    Modeling Scenario
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    1-098-NeuronDetection-ModelingScenario
    Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in mathematical neuroscience as ``integrate-and-fire''...
    biologyneuroscienceneuron physiologyvoltageintegrate and firethrefholscoincidence detectionRC circuit
    Potential Scenario
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    2017-GR_Gustafson-Differential Equations Course Materials
    There are many applications from compartment and cascade analysis, recycling brine tank, home heating with multiple rooms, chemostat, microbes, heartbeats, lidocaine, nutrient flow in an aquarium, biomass transfer, pesticides, forecasting prices,...
    chemostatmicrobesbiomassforecastingtransfercompartmentpesticidesearthquaketankheatinglidocainebrineheartbeatsnutrient flowaquariumelectric networkscircuitsloggingbuildingcascade
    Potential Scenario
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    2018-David_Bourne-Pharmacokinetics – Source Material
    This is a rich source of pharmacokinetics modeling activities and data. These are syllabus notes with homework assignments listed.
    boluspharmacokineticspharmacodynamicdrug distribution
    Potential Scenario
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    1994-Roland_Minton-A Progression of Projectiles-Examples from Sports
    There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,
    sportsresistanceprojectilebaseballdraglinear resistancequadratic resistancetennis
    Article or Presentation
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    2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex
    We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their...
    exponential growthsolutionslinear systemsdecayconjecture
    Article or Presentation
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    1994-Brian_Winkel-Ant_Tunnels_and_Calculus
    A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.
    differential equationsdifference equationfirst orderderivative definitionant tunnel
    Free Online Textbook
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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
    Technique Narrative
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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