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1. 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. 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. 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. 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. 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. 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...

7. 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. 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.

9. 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...

10. 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...

11. 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...

12. 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;...

13. 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...

14. 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...

15. 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...

16. 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,...

17. 07 Sep 2017 | Potential Scenario Ideas

Domokos , Andras. 2017. Differential Equations - Theory and Applications – Notes. 126 pp. California State University, Sacramento.   http://www.csus.edu/indiv/d/domokos/diffeq.pdf . Accessed 6 September 2017.The author says in the Introduction,“Differential Equations is a...

18. 02 Sep 2017 | Potential Scenario Ideas

Ogunrinde, R. B.  and J. Sunday. 2012. On some models based on second order differential equation. American Journal of Scientific and Industrial Research. 3(5): 288-291.Abstract:  This paper presents some models based on second order differential equations. Such models include...

19. 17 May 2017 | Modeling Scenarios

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.

20. 07 Apr 2017 | Modeling Scenarios

We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time with several applications.