## Tags: Integrating Factor

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1. 08 Aug 2021 | | Contributor(s):: Barbara Zubik-Kowal

This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods. On the analytical side, students will solve one of the model equations, describing the first stage of a...

2. 10 Jun 2020 | | Contributor(s):: Brian Winkel

We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module - Modeling the Spread of Oil Slick.This module contains1)  (Below and separate file in Supporting Docs) A brief Teaching Guide with an overview of the content and...

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. 22 Aug 2018 | | Contributor(s):: Norman Loney

We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

5. 27 Nov 2016 | | Contributor(s):: Brian Winkel

We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

6. 19 May 2016 | | Contributor(s):: John Thomas Sieben

Divers, especially novice divers, have concerns about running out of breathing air while at depth.  One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using...

7. 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...

8. 26 Jun 2015 | | Contributor(s):: Jane M. Watson

Watson, Jane M. 1991. Building probability models in a differential equations course. International Journal of Mathematical Education in Science and Technology. 22(4): 507-517.See https://www.tandfonline.com/doi/abs/10.1080/0020739910220402 .Article Abstract: An application is...

9. 26 Jun 2015 | | Contributor(s):: Michael C. Mackey, Leon Glass, William Clark

Mackey,  Michael C. and Leon Glass. 1977. Oscillation and Chaos in Physiological Control Systems. Science. 197: 287-289.See https://www.science.org/doi/abs/10.1126/science.267326 .Article Abstract: First-order nonlinear differential-delay equations describing physiological control...

10. 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...

11. 04 Jun 2015 | | Contributor(s):: Brian Winkel

Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

12. 03 Jun 2015 | | Contributor(s):: Brian Winkel

We present several situations in which differential equation models serve to aid in sleuthing and general investigations. One involves initial speed given information about constant deceleration and distance to stop in traffic incident; one involves modeling a steel ball launched vertically and...

13. 02 Jun 2015 | | Contributor(s):: Brian Winkel

Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.

14. 31 May 2015 | | Contributor(s):: Brian Winkel

We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose.  In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...

15. 30 May 2015 | | Contributor(s):: Brian Winkel

We present a situation in which a chemistry graduate student is assigned the  task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...

16. 30 May 2015 | | Contributor(s):: Brian Winkel

We present a situation in which a chemistry graduate student is assigned the  task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of when...

17. 30 May 2015 | | Contributor(s):: Karen Bliss

18. 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 ...

19. 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.

20. 30 May 2015 | | Contributor(s):: Brian Winkel

We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, collect data, estimate parameters, and compare their model prediction with their actual data. There is a video of one run of the main simulation in...