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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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    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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    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
    Technique Narrative
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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
    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
    Potential Scenario
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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
    Modeling Scenario
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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game.
    zombiesSIR modelsGame
    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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    2011-Lucas_Pulley-Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations
    This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare.
    simulationpredator-preyLotka-VolterrapopulationCanadian LynxSnowshoe Harecritical values
    Technique Narrative
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    5-005-StiffDifferentialEquations-TechniqueNarrative
    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
    Euler's methodexplicit methodsimplicit methodsstiffsitffnessstiff differential equationinstability
    Article or Presentation
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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.
    differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility
    Modeling Scenario
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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
    Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous
    Technique Narrative
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    5-010-MatrixExponential-TechniqueNarrative
    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and...
    matrix esponentialPutzer's Algorithmdiagonalizationeigenvalueseigenvectors
    Potential Scenario
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    2014-Allen-EtAl-Perturbations in Epidemiological Models -When zombies attack we can survive
    In this paper, we investigate the existence of stability-changing bifurcations in epidemiological models used to study the spread of zombiism through a human population.
    epidemiologydynamical systemszombiesbifurcationperturbation
    Free Online Textbook
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    2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology
    I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.
    biologytextbooksystemsdyanmical system
    Potential Scenario
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    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
    dynamical systemsregulationsteady statesales modelexternal stimulus
    Potential Scenario
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    2014-Blomhøj-EtAl-Compartment models
    An overview of compartment models with many rich illustrations and much attention to various numerical methods in solutions of the resulting differential equations using Matlab. Also included is a section on the limitations of compartment models.
    concentrationkineticsphysiologycompartmentsalttankbalancereactionsminkbathtub
    Modeling Scenario
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    7-011-CoupledSystemLaplace-ModelingScenario
    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
    transfer functionpolycarbonatebaby heatercoupled systemheating
    Potential Scenario
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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
    pendulumLotka Volterra equationsexistenceuniqueness
    Article or Presentation
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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow