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    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
    strategies discovery learning eigenvectors eigenvalue
    Technique Narrative
    119

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    30

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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 learning conjecture solution substitution
    Technique Narrative
    391

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    62

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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 esponential Putzer's Algorithm diagonalization eigenvalues eigenvectors
    Modeling Scenario
    47

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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.
    attrition Lanchester model predator-predator N-square Law
    Modeling Scenario
    62

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    1

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    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
    optimization p Yield and sustainability nonprofit management Law of Mass Action kinetic reaction