
1109TEmployeeAttrition
25 Mar 2019  Modeling Scenarios
This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

1063TThreeHoleColumn
15 Dec 2018  Modeling Scenarios
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

1063SThreeHoleColumn
15 Dec 2018  Modeling Scenarios
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
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...

1055TWaterFallingInCone
16 Mar 2018  Modeling Scenarios
We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube. This is an application of Torricelli's Law.

LeakingBucket: Differential Equations in Engineering
03 Mar 2018  Potential Scenario Ideas
Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
18 Jan 2018  Presentations
Incorporating a Modeling First Approach into a Traditional ODE Course by Mike Karls. Ball State University.A talk given at the AMS Special Session on Modeling in Differential Equations  High School, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913...

2000deOliveraEtAlPinholeWaterFlowFromCylindricalBottles
26 Nov 2017  Potential Scenario Ideas
2000. deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite. Pinhole Water Flow From Cylindrical Bottles. Phys.Educ. 35(2): 110119.From the opening of the article, "We performed an experiment on elementary hydrodynamics. The...

2012UrbanoThe Draining of a Plastic Bottle
09 Oct 2017  Potential Scenario Ideas
2012Urbano, Lensyl. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus. Montessori Muddle. http://montessorimuddle.org/2012/05/01/thedrainingofajugintegratingaphysicsexperimentintocalculus/ . Accessed 9 October 2017.Abstract: I punched a small hole...

2000deOliveiraEtAl Pinhole water flow from cylindrical bottles
09 Oct 2017  Potential Scenario Ideas
de Oliveira, Paulo Murilo Castro , Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite. 2000Pinhole water flow from cylindrical bottles. Phys. Educ. 35(2): March. 110119. From the article, “We performed an experiment on elementary hydrodynamics. The basic...

Math Modeling with Differential Equations  Interesting Tank Problem
12 Sep 2017  Potential Scenario Ideas
Math Modeling with Differential Equations  Interesting Tank ProblemMath Modeling with Differential Equations  Interesting Tank Problem . Class Notes on five problems.,Several models are workd out including exponential decay, bullet traveling with resisitance, This material contains a solution...

2001KerleyKnisleyUsing data to motivate models in differential equations
11 Sep 2017  Potential Scenario Ideas
Knisley, Jeff and Lyndell Kerley. 2001. Using data to motivate the models used in introductory differential equations. PRIMUS. 11(20): 111123.Abstract: Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom...

2015UnpropogandaFilling and Draining Spherical Tank
11 Sep 2017  Potential Scenario Ideas
2015UnpropogandaMore on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank. https://unpropaganda.wordpress.com/2015/06/14/moreonfillingasphericaltankandgravitationaldrainageofasphericaltank/ . Accessed 10 September 2017.One of several interesting columns...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017  Potential Scenario Ideas
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.Abstract: Differential equation models for population dynamics are now standard fare in singlevariable calculus. Building on these ordinary differential equation (ODE)...

PennelDifferential Equaitons First Order Applications
09 Sep 2017  Potential Scenario Ideas
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 Law...

1999HaninWhichTankEmptiesFirst
09 Sep 2017  Potential Scenario Ideas
Hanin, Leonid G. 1999. Which tank empties first? The American Mathematical Monthly. 106(10): 943947. Preprint.From the opening of the paper, “Suppose that water towers like those shown in Figure 1 are initially filled with water and have the same volume, height, and...

Math2300Torrielli'LawExercises
08 Sep 2017  Potential Scenario Ideas
Math2300 Torricelli’s Law Exercises. University of Colarado. https://math.colorado.edu/math2300/projects/2300Project12ToricelliSol.pdf . Accessed 7 September 2017.This is a set of completely worked out exercises which could be the basis for a Modeling Scenario based on...

Gustafson2250 EngineeringMathematicsApplications
08 Sep 2017  Potential Scenario Ideas
Gustafson, G. B. Science and Engineering ApplicationsSection 2.8. http://www.math.utah.edu/~gustafso/2250SciEngApplications.pdf . Accessed 8 September 2017.This material is from a wealth of other material authored by Grant B. Gustafson in the Mathematics Department at the University of...

1999KowalczykHausknechtUsing DEs To Model Real World Data
08 Sep 2017  Potential Scenario Ideas
Kowalczyk, Robert E. and Adam O. Hausknecht. 1999. Using Differential Equations to Model RealWorld Data. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics. Reading MA: AddisonWesley Publishing Co. pp. 246250Opening of article,...

2002FayThePendulumEquation
08 Sep 2017  Potential Scenario Ideas
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505519.Abstract:We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it. On the one hand, we suggest that the third and fifthorder Taylor series...