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  1. 3-064-T-GearTrain

    31 Aug 2019 | Modeling Scenarios

    In this scenario students will model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components. Students should have some...

  2. 3-150-T-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios

    This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...

  3. 3-150-S-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios

    This project uses the steady-state 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 steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...

  4. 3-067-T-RLCSeriesCircuit

    28 Apr 2019 | Modeling Scenarios

    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).

  5. 5090-T-SolidParticleErosion

    27 Mar 2019 | Modeling Scenarios

    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...

  6. 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...

  7. 5-005-Text-T-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  8. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | Technique Narratives

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  9. 3-009-T-BallDropInWater

    16 Dec 2018 | Modeling Scenarios

    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.

  10. 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...

  11. 3-095-T-ShotInWater

    05 Apr 2018 | Modeling Scenarios

    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene: Do bullets moving through water slow as dramatically as depicted in the movies, so that someone a few...

  12. Farley and Tiffany - Time to Change our Traditional Differential Equations

    19 Jan 2018 | Presentations

    Time to Change our Traditional Differential Equations By  Rosemary Farley and Patrice Tiffany, Manhattan College.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...

  13. 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...

  14. 2015-Endale-ApplicationsOfODEsToRealWorldSystems

    26 Nov 2017 | Potential Scenario Ideas

    2015. Endale, Mersha Amdie. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the physical...

  15. 2011-Harwood-Modeling a RLC Circuit

    12 Sep 2017 | Potential Scenario Ideas

    Harwood, Kenny. 2011. Modeling a RLC Circuit’s Current with Differential Equations. Paper. 17 pp.Abstract The world of electricity and light have only within the past century been explained in mathematical terms yet still remain a mystery to the human race. R. Buckminster Fuller said;...

  16. 2009-MallettFetbrandt-Differential Equations Class Notes

    11 Sep 2017 | Potential Scenario Ideas

    Mallett, Travis and Josh Fetbrandt. Differential Equations Class Notes. Washington State University.From the Dear Reader opening page of these notes,“These notes were written by two students (Travis Mallett and Josh Fetbrandt) at Washington State University in Fall 2009 and are intended to...

  17. Transient and Steady State response in RC or RL circuits

    11 Sep 2017 | Potential Scenario Ideas

    Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides,This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

  18. 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)...

  19. 2015-PendrillEager-Trampoline Jumping Model

    09 Sep 2017 | Potential Scenario Ideas

    Pendrill. Ann-Marie and David Eager. 2015. Free fall and harmonic oscillations: analyzing trampoline jumps. Physics Education. 50(1): 1-9.http://iopscience.iop.org/article/10.1088/0031-9120/50/1/64/meta . Accessed 5 September 2017. (This is an author-created, un-copyedited version of an...

  20. BobbingObjectInWater

    09 Sep 2017 | Potential Scenario Ideas

    Introduction to Second Order Linear Equations- Bobbing Object in Water. 2 pp.This is a nice treatment of developing a model of a bobbing object in water from first principles with some nice additional questions which would make a nice Modeling Scenario.Keywords:  buoyancy, bobbing, water,...