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3-103-PullBackCars-ModelingScenario

This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.

modeling dynamics hands-on toy pull-back car pullback

Modeling Scenario

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1-001-MM-DeathAndImmigration-ModelingScenario

We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!

simulation immigration death Spanish dats Winkel Brian Winkel

Modeling Scenario

1167

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2908

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3-100-Ripcord-Toys-ModelingScenario

This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.

data physics dynamics data collection rolling slipping ripcord toy

Modeling Scenario

478

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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

849

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762

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1-015-Torricelli-ModelingScenario

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

data Spanish tank column of water aperture Torricelli's Law Conservation of Energyt Solver water flow Excel Solver

Modeling Scenario

933

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340

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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

272

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148

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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

Technique Narrative

150

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2-001-NumericalMethodsComparisons-TechniqueNarrative

This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.

Euler's method improved Euler's method RK3 methods RK4 methods order of accuracy absolute error CPU time

Modeling Scenario

352

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143

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comments

3-043-BallisticModeling-SpongeDart-ModelingScenario

The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.

projectile motion air resistance ballistics dimensional analysis Newtonian mechanics sponge dart Nerf gun Nerf dart Buckingham's Theorem

Modeling Scenario

479

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1-012-Sublimation-Modeling Scenario

We offer data on the sublimation of dry ice (carbon dioxide) collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the...

sublimation dry ice

Modeling Scenario

136

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1-028-SouthernSweetIcedTea-ModelingScenario

We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.

data Newton's Law of Cooling tea sweet tea

Modeling Scenario

125

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1-022-SpreadOfTechnologies-ModelingScenario

We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

data analysis technology logistic spread innovation

Modeling Scenario

115

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1-017-DiseaseSpread-ModelingScenario

Using a grid and m&m candies, we simulate the spread of disease. Students conduct the simulation and collect data to estimate parameters (in several ways) in a differential equation model for the spread of the disease.

Modeling Scenario

125

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1-011A-Kinetics-ModelingScenario

We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.

kinetics Law of Mass Action fitting order of reaction chemical reaction

Modeling Scenario

417

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1-032-WordPropagation-ModelingScenario

This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.

Google exponential growth language word problems etymology Ngram propagation Jumbo