
1102CSCancerGrowth
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 firstorder differential...

1005CSOilSlick
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,...

1165SFlushToilet
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 firstorder, twoparameter separable equation and the solution has a characteristic Sshaped curve or sigmoid curve. The students derive the solution to the model, use least...

1160SHeartDeathRate
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...

9125SBeamModeling
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...

1104SInfectionRisk
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,...

1098SNeuronDetection
25 Aug 2021   Contributor(s):: Joshua Goldwyn
In this activity students will study a linear, first order, onedimensional 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 ``integrateandfire''...

1142SWaterBottles
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...

1134SLanguageDynamics
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...

1135SFishHarvesting
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...

1097SSwimmingPool
08 Aug 2021   Contributor(s):: Barbara ZubikKowal
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...

1150SCancerTherapy
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...

1137SSheepGraze
03 Mar 2021   Contributor(s):: Mary Vanderschoot
One of the most wellknown mathematical models in ecology is the LotkaVolterra predatorprey 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...

1119SDairyFarming
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.

1096SOpAmpDifferentiator
09 Aug 2020   Contributor(s):: Virgil Ganescu
In this validationoriented 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...

1088SRoomTemperature
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...

1136SMarriageAge
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 firstorder ordinary differential equations (which...

1128SRocketFlight
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.

1124SWorldPopulation
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 xySTitleStudentVersionCzech.

10001STilingHallway
12 Sep 2019   Contributor(s):: Rob Krueger, Eric Stachura
Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration. Then students will be introduced to the concept of the shift...