## Tags: differential

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1. 27 Jun 2016 | | Contributor(s):: Brian Winkel

We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice. Collected data on generation or iteration and population  is then...

2. 18 Jun 2019 | | Contributor(s):: Dina Yagodich

This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

3. 03 Jul 2019 | | Contributor(s):: Dina Yagodich

We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

4. 12 May 2015 | | Contributor(s):: Brian Winkel

We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.

5. 10 Jan 2019 | | Contributor(s):: Brian Winkel

We ask students to develop two numerical methods for solving first order differential equations  geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes.

6. 30 May 2015 | | Contributor(s):: Brian Winkel

We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

7. 30 May 2015 | | Contributor(s):: Brian Winkel

We describe a modeling activity for students in  which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...

8. 30 May 2015 | | Contributor(s):: Karen Bliss

9. 17 Jan 2022 | | Contributor(s):: Jennie D'Ambroise

We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate. This model enlightens students as to how derivatives are used in applications as well as a brief introductory encounter with parameter estimation for a linear,...

10. 17 Mar 2017 | | Contributor(s):: Brian Winkel

We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''

11. 24 Jan 2016 | | Contributor(s):: Rachel Bayless, Nathan Pennington

This activity is structured as a letter from a company seeking assistance with a mathematical problem. The students will act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use...

12. 27 Nov 2015 | | Contributor(s):: Brian Winkel

We examine  plots on the  spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

13. 06 May 2016 | | Contributor(s):: David Culver

This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...

14. 04 Jun 2015 | | Contributor(s):: Brian Winkel

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...

15. 25 Jun 2016 | | Contributor(s):: Troy Henderson

We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea.  We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.

16. 02 Mar 2016 | | Contributor(s):: Sania Qureshi

We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom  is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

17. 17 Aug 2018 | | Contributor(s):: Therese Shelton

We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

18. 07 Apr 2016 | | Contributor(s):: Rachelle DeCoste, Rachel Bayless

This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.

19. 24 Dec 2015 | | Contributor(s):: Eric Sullivan, Elizabeth Anne Carlson

This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...

20. 03 Jun 2016 | | Contributor(s):: John Thomas Sieben

Things float or they don’t.  Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...