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1. 28 May 2020 | Modeling Scenarios

This is a situation where the student is a young tech staff member in a company and is charged with anlyzing costs for a spring to meet certain specifications.

2. 26 Mar 2020 | Potential Scenario Ideas | Contributor(s): Brian Winkel

Beeken-FirstOrderDifferentialEquations-AirResistanceBeeken, Paul. First Order Differential Equations  as applied to Air Resistance. Byram Hills High School.This is a nice and gentle introduction to air resistance modeling.From the Introduction"The problem of air...

3. 24 Mar 2020 | Modeling Scenarios | Contributor(s): Brian Winkel

We are given data on a falling Styrofoam ball and we seek to model this motion.

4. 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.

5. 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...

6. 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 often...

7. 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. 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 January...

9. 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. 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 resistant...

11. 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. 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. 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. 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. 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. 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. 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.

18. 02 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437-440.Article Abstract: NONEThis paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height...

19. 01 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

Peastrel, M., R. Lynch, and A. Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511-513.Article Abstract: We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and...

20. 01 Mar 2017 | Articles and Publications | Contributor(s): Brian Winkel

Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442-444.We quote from the article,“The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick. . . . The goals of the experiment include fostering...