
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...

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...

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.

2018McCarthy, C.  Newton's Law of Cooling.
01 Apr 2020   Contributor(s):: Brian Winkel
McCarthy, C. 2018. Newton’s Law of Cooling.See https://mccarthymat501.commons.gc.cuny.edu/newtoniancooling/ .Active classroom scenario with stepbystep procedure, data, R code. Scenario: You have hot water (initial temperature ) in a container, say a cup....

3015SStyrofoamBallFall
24 Mar 2020   Contributor(s):: Brian Winkel
We are given data on a falling Styrofoam ball and we seek to model this motion.

2003Ellermeyer, S. F.  Modeling Via Differential Equations
12 Mar 2020   Contributor(s):: Brian Winkel
2003. Ellermeyer, S. F. Modeling Via Differential Equations  preprint.Abstract: Mathematical modeling via differential equations is introduced. We partially follow the approach in Section 1.1 of the Blanchard, Devaney, and Hall text book.

9020SHeatDiffusion
14 Oct 2019   Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

1068SWaterBottleCooling
14 Aug 2019   Contributor(s):: Eli E Goldwyn
The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room. The goal is for the students to understand...

3150SItsABlastFurnace
13 Aug 2019   Contributor(s):: Kurt Bryan
This project uses the steadystate heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steadystate, so that only an elementary ordinary differential equation (ODE) is needed, and...

5090SSolidParticleErosion
27 Mar 2019   Contributor(s):: Richard R Laverty
By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface. Examination of the solution will yield a formula for the...

3043SBallisticModelingSpongeDart
20 Nov 2018   Contributor(s):: Jean Marie Linhart, Peter Howard
The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance. The first two models are based respectively on the common simplifying assumptions of no air resistance and...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

2018Ding, Wandi  Experience and Lessons Learned from Using SIMIODE Modeling Scenarios
19 Jan 2018   Contributor(s):: Wandi Ding
Experience and Lessons Learned from Using SIMIODE Modeling ScenariosBy Wandi Ding, Ryan Florida, Jeffrey Summers, Puran Nepal, Middle Tennesse State UniversityA talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear...

2017Pennel, Steve  Differential Equations First Order Applications  Notes
09 Sep 2017   Contributor(s):: Brian Winkel
Pennel, Steve. Differential Equations: Applications of First Order Differential Equations. Notes. 44 p. Universiyt of Massachusetts, Lowel.This is a set of modeling activities with derivations, Matlab code, and mathematical details covering the following topics: Newton’s Second...

2017Groetsch, C. W.  Hammer and Feather: Some Calculus of Mass and Fall Time
09 Sep 2017   Contributor(s):: Brian Winkel
Groetsch, C. W. 2017. Hammer and Feather: Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 37.See https://www.tandfonline.com/doi/abs/10.4169/math.mag.90.1.3 .The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA...

1115SModelingWithFirstOrderODEs
04 Sep 2017   Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model

1043SCoolingUpAndDown
26 Aug 2017   Contributor(s):: Brian Winkel
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

2011Leinbach, Carl  Beyond Newton's law of cooling – estimation of time since death
02 Mar 2017   Contributor(s):: Brian Winkel
Leinbach, Carl. 2011. Beyond Newton’s law of cooling – estimation of time since death. International Journal of Mathematical Education in Science and Technology. 42(6): 765774.Article Abstract: The estimate of the time since death and, thus, the time of death is strictly that, an...

3065SUpDown
05 Oct 2016   Contributor(s):: Brian Winkel

1061SPotatoCooling
05 Oct 2016   Contributor(s):: Brian Winkel
We model the cooling of a baked potato and compare it to studentcollected data.