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SIMIODE

Resources

Includes clear efforts on Issues
Modeling Scenario
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1-038-Ebola-ModelingScenario
Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
population dynamics data analysis exponential growth Ebola logistic epidemic
Modeling Scenario
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66

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1-128-RocketFlight-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
resistance Flight Rocketry mass Newton's Second Law of Motion thrust Free Body Diagram apex rocket
Modeling Scenario
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41

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1-078-MonodGrowthModel-ModelingScenario
Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
bacteria nutrient cycles growth Monod consumption
Modeling Scenario
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107

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1-031-CoolIt-ModelingScenario
We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
Spanish Newton's Law of Cooling cooling
Modeling Scenario
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69

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1-005-OilSlick-ModelingScenario
We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
model fitting spreadsheets Spanish derrame de petrÃ³leo datos expansiÃ³n oil slick
Modeling Scenario
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116

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1-007-AntTunnelBuilding-ModelingScenario
We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill.
Spanish hormiga tÃºnel ant tunnel
Modeling Scenario
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51

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1-008-HangTime-ModelingScenario
We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''
gravity hang tim Newton's Second Law of Motion jump shot
Modeling Scenario
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135

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6-001-Epidemic-ModelingScenario
This paper presents real-world data, a problem statement, and discussion of a common approach to modeling that data, including student responses. In particular, we provide time-series data on the number of boys bedridden due to an outbreak of...
data difference equations parameter estimation continuous epidemic discrete boarding school
Modeling Scenario
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483

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3-065-UpDown-ModelingScenario
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity Newton's Second Law of Motion velocity motion apex
Modeling Scenario
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56

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1-145-FastPitch-ModelingScenario
We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
Measurement resistance air resistance baseball pitcher fast
Technique Narrative
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1-015-DimensionlessVariables-TechniqueNarrative
This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
linearization dimensional analysis time scale scaling dimensionless variables spatial scale
Technique Narrative
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34

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7-006-LaplaceTransformBirth-TechniqueNarrative
We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
Transformations power series
Technique Narrative
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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
115

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30

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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.
computation error Torricelli's Law data fitting linear approximation
Technique Narrative
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31