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1-190-S-IntroClass
05 Mar 2022 | Modeling Scenarios | Contributor(s):: Bill Skerbitz
Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...
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1-145-S-FastPitch
23 Jan 2022 | Modeling Scenarios | Contributor(s):: Erich McAlister
Pitch velocity is one of the most fascinating statistics in baseball, as documented in the 2015 documentary Fastball. Modern measurements of pitch velocity are taken as the maximum velocity achieved at any point between the pitcher's hand and home plate. However, the velocity of the ball...
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4-036-S-AltitudeDependentGravity
22 Jan 2022 | Modeling Scenarios | Contributor(s):: Jakob Kotas
Basic projectile motion without air resistance typically assumes gravity is constant. In reality, the acceleration due to gravity is proportional to the inverse-square of the distance between the centers of mass of the Earth and the projectile. When projectiles are near to Earth's surface,...
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4-039-S-FallingDarts
21 Jan 2022 | Modeling Scenarios | Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...
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1-102C-S-CancerGrowth
19 Jan 2022 | Modeling Scenarios | Contributor(s):: Jennie D'Ambroise, Jue Wang
This module is designed for Calculus I class and guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and Gompertz....
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1-005C-S-OilSlick
17 Jan 2022 | Modeling Scenarios | Contributor(s):: Jennie D'Ambroise
We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate. This model enlightens students as to how derivatives are used in applications as well as a brief introductory encounter with parameter estimation for a linear,...
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3-091-S-MassSpringExperiments
14 Jan 2022 | Modeling Scenarios | Contributor(s):: Bonnie Moon
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data. Before this lab, students should have modeled spring-mass systems and solved second-order...
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1-170-S-CensusModeling-StudentVersion
22 Dec 2021 | Modeling Scenarios | Contributor(s):: Jean Marie Linhart, Gary William Epp
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. We will compare and contrast the United States census data and the...
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1-165-S-FlushToilet
18 Oct 2021 | Modeling Scenarios | Contributor(s):: Maila Hallare, Charles Lamb
This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve. The students derive the solution to the model, use least...
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1-160-S-HeartDeathRate
20 Sep 2021 | Modeling Scenarios | Contributor(s):: Arati Nanda Pati
In this modeling scenario, we offer students simulation experience from a given data set which represents the heart death rate during the period 2000 - 2010 using several approaches to include exponential decay, difference equation, differential equation, and parameter estimation using EXCEL. We...
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9-030-S-WaterHammer
31 Aug 2021 | Modeling Scenarios | Contributor(s):: Panagiotis D. Scarlatos
The students will develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs). The equations involved are nonlinear and of hyperbolic type. The problem to be solved is an initial-boundary value problem that describes the time evolution of...
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6-075-S-LorenzSystemSimulation
27 Aug 2021 | Modeling Scenarios | Contributor(s):: Vladimir Riabov
The Lorenz system will be examined by students as a simple model of chaotic behavior (also known as strange attractor). MATLAB code has been created to find the numerical solutions of the Lorenz’ system of nonlinear ordinary differential equations using various parameters, as well as to...
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9-125-S-BeamModeling
27 Aug 2021 | Modeling Scenarios | Contributor(s):: Brody Dylan Johnson
This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided in the student version. A mathematical model for the beam deflection will be...
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1-104-S-InfectionRisk
26 Aug 2021 | Modeling Scenarios | Contributor(s):: Qingxia Li
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions. This project was designed for an introductory section in Calculus II or a course involving ordinary differential equations,...
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1-098-S-NeuronDetection
25 Aug 2021 | Modeling Scenarios | Contributor(s):: Joshua Goldwyn
In this activity students will study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can be used to understand basics of neural dynamics. The modeling framework is known in the mathematical neuroscience literature as the ``integrate-and-fire''...
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1-142-S-WaterBottles
22 Aug 2021 | Modeling Scenarios | Contributor(s):: Brody Dylan Johnson, Elodie Pozzi
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. The modeling scenario leads the students through an...
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1-100-S-EngineeringDemographics
20 Aug 2021 | Modeling Scenarios | Contributor(s):: Brody Dylan Johnson, Elodie Pozzi
The goal of this activity is to show students how population models can be used to examine social issues. The students will examine three different population models and will use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women...
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10-100-S-InsectOutbreaks
17 Aug 2021 | Modeling Scenarios | Contributor(s):: Jacob Paul Duncan
The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warmer weather has allowed MPB populations to achieve synchronous emergence and successful...
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4-065-S-GasInjection
14 Aug 2021 | Modeling Scenarios | Contributor(s):: Vladimir Riabov
Students will use computer programs (or create their own programming code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary conditions. The uniform...
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3-069-S-HeatInBar
12 Aug 2021 | Modeling Scenarios | Contributor(s):: Yuxin Zhang
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches. A series of experiments are designed to study the effects of materials, ambient fluid flows, geometric characteristics, and...