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  1. 1-135-FishHarvesting-ModelingScenario

    1-135-FishHarvesting-ModelingScenario

    2022-05-22 16:53:36 | Teaching Materials | Contributor(s): Jennifer Crodelle | doi:10.25334/Z325-NQ62

    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the rate of harvesting fish.

  2. 1-136-MarriageAge-ModelingScenario

    1-136-MarriageAge-ModelingScenario

    2022-05-22 16:54:19 | Teaching Materials | Contributor(s): Tracy Weyand | doi:10.25334/YGJ9-7093

    Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these models,

  3. 1-137-SheepGraze-ModelingScenario

    1-137-SheepGraze-ModelingScenario

    2022-05-22 16:55:00 | Teaching Materials | Contributor(s): Mary Vanderschoot | doi:10.25334/MEH9-1E64

    In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas for the herbivore consumption rate.

  4. 5-026-Evictions-MmodelingScenario

    5-026-Evictions-MmodelingScenario

    2022-05-22 16:52:51 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/1998-8110

    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .

  5. 1-138-InnerEarDrugDelivery-ModelingScenario

    1-138-InnerEarDrugDelivery-ModelingScenario

    2022-05-22 13:52:50 | Teaching Materials | Contributor(s): Jue Wang | doi:10.25334/F9HH-FK88

    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.

  6. 5-076-LanchesterLaws-ModelingScenario

    5-076-LanchesterLaws-ModelingScenario

    2022-05-22 13:38:18 | Teaching Materials | Contributor(s): Blain Patterson | doi:10.25334/XM37-6W26

    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,

  7. 1-139-PlantsVsHerbivores-ModeliongScenario

    1-139-PlantsVsHerbivores-ModeliongScenario

    2022-05-22 13:27:04 | Teaching Materials | Contributor(s): Mary Vanderschoot | doi:10.25334/PHTV-XY94

    In this activity, students will apply a variety of techniques for analyzing nonlinear systems (e.g., nullclines, linearization, and technologies for drawing phase portraits) to study plant-herbivore models.

  8. 1-140-LeakyBucket-ModelingScenario

    1-140-LeakyBucket-ModelingScenario

    2022-05-22 12:43:06 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/B01H-KG54

    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.

  9. 1-141-MMGameRevisited-ModelingScenario

    1-141-MMGameRevisited-ModelingScenario

    2022-05-22 12:43:47 | Teaching Materials | Contributor(s): Mehdi Hakim-Hashemi | doi:10.25334/NDP4-9K94

    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen M&M falling M up when tossed).

  10. 1-142-WaterBottles-ModelingScenario

    1-142-WaterBottles-ModelingScenario

    2022-05-22 12:44:33 | Teaching Materials | Contributor(s): Brody Dylan Johnson, Elodie Pozzi | doi:10.25334/5HB5-2287

    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.

  11. 1-143-PopulationModelVariationsMATLAB-ModelingScenario

    1-143-PopulationModelVariationsMATLAB-ModelingScenario

    2022-05-22 12:45:14 | Teaching Materials | Contributor(s): William (Bill) Skerbitz | doi:10.25334/8PE1-0732

    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.

  12. 1-150-CancerTherapy-ModelingScenario

    1-150-CancerTherapy-ModelingScenario

    2022-05-22 12:46:05 | Teaching Materials | Contributor(s): Iordanka Panayotova, Maila Hallare | doi:10.25334/ZYJC-4B04

    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.

  13. 1-160-HeartDeathRate-ModelingScenario

    1-160-HeartDeathRate-ModelingScenario

    2022-05-22 12:46:53 | Teaching Materials | Contributor(s): Arati Nanda Pati | doi:10.25334/E6JE-KH07

    Students simulate 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.

  14. 1-001a-MMDeathImmigration-Variation-ModelingScenario

    1-001a-MMDeathImmigration-Variation-ModelingScenario

    2022-05-22 12:47:38 | Teaching Materials | Contributor(s): Laren Bliss | doi:10.25334/KV3D-K711

    We model exponential death with m&m's as well as death with immigration.

  15. 1-165-FlushToilet-ModelingScenario

    1-165-FlushToilet-ModelingScenario

    2022-05-22 12:48:26 | Teaching Materials | Contributor(s): Maila Hallare, Charles Lamb | doi:10.25334/KX0G-8N50

    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.

  16. 1-170-CensusModeling-ModelingScenario

    1-170-CensusModeling-ModelingScenario

    2022-05-22 12:49:10 | Teaching Materials | Contributor(s): Gary William Epp, Jean Marie Linhart | doi:10.25334/MB13-B278

    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.

  17. 1-190-IntroClass-ModelingScenario

    1-190-IntroClass-ModelingScenario

    2022-05-22 12:49:57 | Teaching Materials | Contributor(s): William (Bill) Skerbitz | doi:10.25334/8DBV-A022

    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.

  18. 3-001-SpringMassDataAnalysis-ModelingScenario

    3-001-SpringMassDataAnalysis-ModelingScenario

    2022-05-22 12:50:45 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/W79E-P417

    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.

  19. 3-002-ModelsMotivatingSecondOrder-ModelingScenario

    3-002-ModelsMotivatingSecondOrder-ModelingScenario

    2022-05-22 12:51:32 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/9HJT-NG71

    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.

  20. 3-004-VanderPol-ModelingScenario

    3-004-VanderPol-ModelingScenario

    2022-05-22 12:52:18 | Teaching Materials | Contributor(s): Mark Lau Kwan | doi:10.25334/150W-J928

    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.