Tags: order

Modeling Scenarios (1-20 of 84)

  1. 1-190-S-IntroClass

    05 Mar 2022 | | 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. 1-102C-S-CancerGrowth

    19 Jan 2022 | | 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...

  3. 1-005C-S-OilSlick

    17 Jan 2022 | | 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,...

  4. 1-165-S-FlushToilet

    18 Oct 2021 | | 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...

  5. 1-160-S-HeartDeathRate

    20 Sep 2021 | | 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...

  6. 9-125-S-BeamModeling

    27 Aug 2021 | | 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...

  7. 1-104-S-InfectionRisk

    26 Aug 2021 | | 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,...

  8. 1-098-S-NeuronDetection

    25 Aug 2021 | | 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''...

  9. 1-142-S-WaterBottles

    22 Aug 2021 | | 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...

  10. 1-134-S-LanguageDynamics

    08 Aug 2021 | | Contributor(s):: Jennifer Crodelle

    Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another. By answering a list of questions, students will explore how changing the status of a language will alter the...

  11. 1-135-S-FishHarvesting

    08 Aug 2021 | | Contributor(s):: Jennifer Crodelle

    This modeling scenario will introduce students to the concept of a bifurcation through a fish harvesting model. 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...

  12. 1-097-S-SwimmingPool

    08 Aug 2021 | | Contributor(s):: Barbara Zubik-Kowal

    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods. On the analytical side, students will solve one of the model equations, describing the first stage of a...

  13. 1-150-S-CancerTherapy

    03 Aug 2021 | | Contributor(s):: Maila Hallare, Iordanka Panayotova

    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.Activities will help students appreciate the importance of...

  14. 1-137-S-SheepGraze

    03 Mar 2021 | | Contributor(s):: Mary Vanderschoot

    One of the most well-known mathematical models in ecology is the Lotka-Volterra predator-prey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and...

  15. 1-119-S-DairyFarming

    20 Sep 2020 | | Contributor(s):: Rob Krueger

    A simple first order population growth model is presented.  The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.

  16. 1-096-S-OpAmpDifferentiator

    09 Aug 2020 | | Contributor(s):: Virgil Ganescu

    In this validation-oriented setup, the output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and the results are compared with the data acquired from analyzing the numerical...

  17. 1-088-S-RoomTemperature

    15 Jun 2020 | | Contributor(s):: Tracy Weyand

    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...

  18. 1-136-S-MarriageAge

    11 Jun 2020 | | Contributor(s):: Tracy Weyand

    Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...

  19. 1-128-S-RocketFlight

    04 Jun 2020 | | Contributor(s):: Brian Winkel

    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 fall to earth.

  20. 1-124-S-WorldPopulation

    30 May 2020 | | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel

    We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION  We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be x-y-S-Title-StudentVersion-Czech.