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Vision and Change Core Competencies - Ability

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Includes clear efforts on Issues

Modeling Scenario

340

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113

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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

934

views

340

downloads

comments

1-030-EyeModel-ModelingScenario

We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina.

retinal surgery Akaike Information Criterion Spanish sum of square errors surgery retiona ophthalmology eye intraocular gas bubble

Modeling Scenario

870

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3258

downloads

comments

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 petróleo datos expansión oil slick

Modeling Scenario

507

views

510

downloads

comments

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 túnel ant tunnel

Modeling Scenario

848

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1033

downloads

comments

1-070-FisheryHarvest-ModelingScenario

Students model with logistic growth, harvesting, and diffusion in analyzing ocean fisheries of the Atlantic cod. We help students build models, ever more complex, to capture physical realities. At each stage we ask students to reflect on the model.

logistic Diffusion management harvest fishery

Modeling Scenario

272

views

148

downloads

comments

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

898

views

485

downloads

comments

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

180

views

downloads

comments

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

Modeling Scenario

152

views

150

downloads

comments

1-076-ClimateBifurcation-ModelingScenario

We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.

energy balance climate energy albedo Hysteresis bifurcation ice-age greenhouse balance Stefan Boltzmann Law

Modeling Scenario

204

views

downloads

comments

3-104-BungeeJumping-ModelingScenario

In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.

design falling mass spring\ bungee elesticity recommendation consult

Technique Narrative

135

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downloads

comments

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

133

views

downloads

comments

9-001-SkinBurnModelNumericalMethods-TechniqueNarrative

The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.

Maternal-Fetal interface heat equation Conservation of Energyt heat flux Euler's forward method central difference skin burn hyperthermia thermal conductivity layers

Modeling Scenario

149

views

downloads

comments

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 function polycarbonate baby heater coupled system heating

Technique Narrative

551

views

downloads

comments

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

168

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downloads

comments

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