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...
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...
22 Dec 2021 | | 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...
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,...
20 Aug 2021 | | 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...
04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...
30 Oct 2020 | | Contributor(s):: Brian Winkel
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.
06 May 2020 | | Contributor(s):: Will Mitchell
We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not necessarily mathematicians).
02 Sep 2019 | | Contributor(s):: Jeff Pettit
Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...
31 Aug 2019 | | Contributor(s):: Bill Skerbitz
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...
08 Aug 2019 | | Contributor(s):: Eric Stachura
This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion. Students will explore various Mathematica modules...
17 Feb 2019 | | Contributor(s):: Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...
18 Aug 2018 | | Contributor(s):: Natali Hritonenko
The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks:...
29 Jul 2018 | | Contributor(s):: Jue Wang
This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...
09 Jun 2018 | | Contributor(s):: Randy Boucher, Ryan Edmund Miller
Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...
23 Nov 2016 | | Contributor(s):: Brian Winkel
We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters.
22 Jun 2016 | | Contributor(s):: Troy Henderson
We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat. This data can be used to model and predict the amount...
06 May 2016 | | Contributor(s):: David Culver
This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...
27 Nov 2015 | | Contributor(s):: Brian Winkel
We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.
04 Jun 2015 | | Contributor(s):: Brian Winkel
We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.