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Modeling Scenarios feed

  1. 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...

  2. 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...

  3. 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,...

  4. 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...

  5. 1-102C-S-CancerGrowth

    19 Jan 2022 | Modeling Scenarios | Contributor(s):: Jennie D'Ambroise

    This module 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. Students solve first-order differential...

  6. 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,...

  7. 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...

  8. 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...

  9. 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...

  10. 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...

  11. 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...

  12. 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...

  13. 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...

  14. 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,...

  15. 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''...

  16. 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...

  17. 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...

  18. 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...

  19. 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...

  20. 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...