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SIMIODE

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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
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35

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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
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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
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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.
nullclines pharmacokinetics digoxin drug elimination two compartment
Modeling Scenario
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3-026-SpringInverseProblem-ModelingScenario
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
data mass inverse problem spring\ parameter estimate
Modeling Scenario
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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 resistance directed buoyancy free fall static equilibrium displacement
Modeling Scenario
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3-031-SpringCost-ModelingScenario
We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.
design unit cost spring constant static equilibrium spring masss dashpot
Modeling Scenario
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5-025-SaltCompartments-ModelingScenario
Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
compartment salt tanks
Modeling Scenario
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6-004-VillageEpidemic-ModelingScenario
Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.
SIR models epidemic susceptible infective removed Eyam English village
Modeling Scenario
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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.
dynamics flow conserved fixed points cyclet internet platform diverghence Jacobian attracting repelling nodes stable saddle spiral