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  1. 1-109-T-EmployeeAttrition

    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 first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

  2. 1-063-T-ThreeHoleColumn

    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.

  3. 1-063-S-ThreeHoleColumn

    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.

  4. 6-070-T-BeerBubbles

    24 Apr 2018 | Modeling Scenarios

    The goal of this project is to set up and numerically solve a first-order 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...

  5. 1-055-T-WaterFallingInCone

    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.

  6. 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...

  7. 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, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13...

  8. 2000-deOliveraEtAl-PinholeWaterFlowFromCylindricalBottles

    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): 110-119.From the opening of the article,  "We performed an experiment on elementary hydrodynamics. The...

  9. 2012-Urbano-The Draining of a Plastic Bottle

    09 Oct 2017 | Potential Scenario Ideas

    2012-Urbano, Lensyl. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus.  Montessori Muddle. http://montessorimuddle.org/2012/05/01/the-draining-of-a-jug-integrating-a-physics-experiment-into-calculus/ . Accessed 9 October 2017.Abstract: I punched a small hole...

  10. 2000-deOliveiraEtAl- Pin-hole 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. 2000Pin-hole water flow from cylindrical bottles.  Phys. Educ. 35(2): March.  110-119. From the article, “We performed an experiment on elementary hydrodynamics. The basic...

  11. 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...

  12. 2001-KerleyKnisley-Using 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): 111-123.Abstract: Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom...

  13. 2015-Unpropoganda-Filling and Draining Spherical Tank

    11 Sep 2017 | Potential Scenario Ideas

    2015-Unpropoganda-More on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank. https://unpropaganda.wordpress.com/2015/06/14/more-on-filling-a-spherical-tank-and-gravitational-drainage-of-a-spherical-tank/ . Accessed 10 September 2017.One of several interesting columns...

  14. 2012-Kerckhove-Mathematica Pop Dynamics Tutorial PDE

    10 Sep 2017 | Potential Scenario Ideas

    Kerckhove, Michael.  2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE)...

  15. Pennel-Differential 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...

  16. 1999-Hanin-WhichTankEmptiesFirst

    09 Sep 2017 | Potential Scenario Ideas

    Hanin, Leonid G. 1999. Which tank empties first?  The American Mathematical Monthly.  106(10): 943-947.  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...

  17. Math2300-Torrielli'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...

  18. Gustafson-2250 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...

  19. 1999KowalczykHausknecht-Using 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 Real-World Data. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics.  Reading MA: Addison-Wesley Publishing Co. pp. 246-250Opening of article,...

  20. 2002-Fay-ThePendulumEquation

    08 Sep 2017 | Potential Scenario Ideas

    Fay, T. 2001.The Pendulum Equation.  Int. J. Math. Educ. Sci. Technology.  33(4): 505-519.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 fifth-order Taylor series...