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    Technique Narrative
    460

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    211

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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
    165

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    54

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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
    Modeling Scenario
    320

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    335

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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
    488

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    163

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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
    Modeling Scenario
    292

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    181

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    3-075-RLCCircuits-ModelingScenario
    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.
    resistancecircuitvoltageinductancecapacitancecurrentKirchhoff's Law
    General Resource
    1053

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    139

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    Instructor Solutions Second Edition SIMIODE Textbook HTML Version
    This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
    textbookhtmlSIMIODE textbookSecond Edition
    Article or Presentation
    5854

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    767

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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
    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
    139

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    79

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing
    Modeling Scenario
    245

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    141

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    3-027-BobbingDropping-ModelingScenario
    We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
    drug resistancedirectedbuoyancyfree fallstatic equilibriumdisplacement
    Modeling Scenario
    265

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    549

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    6-065-InternetPlatformUsers-ModelingScenario
    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system.
    dynamicsflowconservedfixed pointscycletinternet platformdiverghenceJacobianattractingrepellingnodesstablesaddlespiral
    Potential Scenario
    144

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    59

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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Potential Scenario
    148

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    54

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    2009-James_May-Nonlinear vibration control of long flexible structures
    An automated, non-linear control scheme was developed to transfer energy from the fundamental vibration mode, where most vibration energy of the structures of interest resides, to higher order modes where vibration impedance was shown to be...
    vibrationdampingtuned mass damperviscousnodalmodel dampingflexible structureenergy transfer
    Potential Scenario
    153

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    75

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    2017-David_Morin-Oscillations
    So needless to say, an understanding of oscillations is required for an understanding of waves.
    dampingfrequency responseresonanceoscillationbeatsunderdampingharmonic oscillatorsover dampingcritical damping
    Modeling Scenario
    271

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    164

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    5-025-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
    compartmentsalttanks