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##### Includes clear efforts on Issues
Modeling Scenario
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##### 1-138-InnerEarDrugDelivery-ModelingScenario
Students examine local drug delivery to the cochlea. The delivery system is modeled as a liquid mixing problem. Students formulate the differential equation, and solve the equation using separation of variables or integrating factor.
concentration drug delivery inner ear cochlea hearing loss
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##### 5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws sensitivity analysisanalysis
Modeling Scenario
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##### 1-142-WaterBottles-ModelingScenario
This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version.
data collection experiment half-life Newton's Law of Cooling water bottle
Modeling Scenario
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##### 1-150-CancerTherapy-ModelingScenario
This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
population dynamics phage therapy exponential growth cancer water treatment decay surgery
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##### 1-170-CensusModeling-ModelingScenario
Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use.
logistic growth exponential population U.S. Census Data assumption Google Sheets Unites States Guatemala
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##### 1-190-IntroClass-ModelingScenario
Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.
population dynamics predator-prey logistic exponential graphical interpretations qualitative analysis
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##### 3-001-SpringMassDataAnalysis-ModelingScenario
We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.
data damping spring-mass system Newton's Second Law of Motion spring constant Hooke's Law
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##### 3-002-ModelsMotivatingSecondOrder-ModelingScenario
Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.
resistance spring mass oscillation Hooke's Law dampening
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##### 3-006-Buoyancy-ModelingScenario
We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.
data collection experiment buoyancy Newton's Second Law of Motion
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##### 3-009-BallDropInWater-ModelingScenario
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
resistance gravity falling body terminal velocity buoyancy
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##### 3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy mass-spring system kinetic energy potential energy total energy
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##### 3-011-EulerBallThrowing-ModelingScenario
If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
coding dragon Vectors Euler's method ball
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##### 3-013-WhiffleBallFall-ModelingScenario
We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.
Akaike Information Criterion resistance gravity Free Body Diagram force falling object Whiffle ball
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##### 3-015-StyrofoamBallFall-ModelingScenario
We are given data on a falling Styrofoam ball and we seek to model this motion.
football resistance gravity falling body sum of square errors Newton's Second Law of Motion sum of forces styrofoam
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