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1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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. 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. 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. 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. 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. 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...