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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. 3-009-T-BallDropInWater

    16 Dec 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

  3. 3-009-S-BallDropInWater

    16 Dec 2018 | Modeling Scenarios | Contributor(s): Brian Winkel

    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

  4. 2008-Will-Hansen-ExamplesOfODEsInPhysics

    09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Witt-Hansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

  5. 2004-PhoebusReily-TheParachuteProblem

    09 Dec 2018 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Phoebus, Ronald and Cole Reilly. 2004, Differential Equations and the Parachute Problem. Presentation 10 May 2004.  https://mse.redwoods.edu/darnold/math55/DEproj/sp04/coleron/presentation.pdf .Abstract: The parachute problem is a classical first semester differential equations problem...

  6. 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...

  7. Modeling Falling Bodies

    01 Mar 2018 | Articles and Publications | Contributor(s): Brian Winkel

    Modelling falling bodies is discussed using a computer algebra system-calculator and introducing various traditional and elementary methods from calculus as well as  numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...

  8. 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...

  9. Pretty Good Physics

    13 Nov 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    We were introduced to PrettyGood Physics  by a high school physics teacher colleague, Paul Beeken, Physics, Byram Hills High School, Armonk NY USA.  He has posted some very nice materials there on differential equations. All the material at this website is free and...

  10. 2006-LoydWodarz Drug Resistance in Acute Viral Infections

    18 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Loyd, Alun L. and Dominik Wodarz.  2006. Drug Resistance in Acute Viral Infections:  Rhinovirus as a Case Study.  Preprint. 21 pp. http://www4.ncsu.edu/~allloyd/pdf_files/resistance_preprint.pdf . Accessed 18 September 2017.Abstract:  The emergence and spread of drug...

  11. 1994-Minton-Progression of Projectiles - Examples from Sports

    12 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Minton, Roland. 1994. A Progression of Projectiles - Examples from Sports. The College Mathematics Teacher. 28(5): 436-442.There is a progression of complexity and issues in projectile motion modeling from no rsistance, to resistance proportional to velocity, then to velocity...

  12. Math Modeling with Differential Equations - Interesting Tank Problem

    12 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    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...

  13. Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations

    10 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Calculus for Engineers II-Sample Problems on mathematical modeling with differential equations. https://www.maths.tcd.ie/~manuela/Sample_1.pdf . Accessed 10 September 2017.Five modeling activities involved with emptying various tanks, projectile motion with resistance, and population growth and...

  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. 2017-Groetsch-HammerANDFeather

    09 Sep 2017 | Potential Scenario Ideas | Contributor(s): Brian Winkel

    Groetsch, C. W. 2017. Hammer and Feather:  Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 3-7.The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a...

  16. 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...

  17. 3-075-T-RLCCircuit

    17 May 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices. We build a differential equation using Kirchhoff's Law and solve and interpret our solutions.

  18. 3-075-S-RLCCircuit

    17 May 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

  19. 3-002-T-ModelsMotivatingSecondOrder

    30 Mar 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...

  20. 3-017-T-StackedCoffeeFiltersFalling

    11 Mar 2017 | Modeling Scenarios | Contributor(s): Brian Winkel

    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered for analysis. Students first form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.