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1. 31 Mar 2019 | Technique Narratives

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

2. 31 Mar 2019 | Technique Narratives

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

3. 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...

4. 04 Mar 2019 | Modeling Scenarios

We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...

5. 17 Feb 2019 | Modeling Scenarios

Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations.  They will also work with other utilities...

6. 17 Feb 2019 | Modeling Scenarios

Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations.  They will also work with other utilities...

7. 10 Jan 2019 | Technique Narratives

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.

8. 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.

9. 09 Dec 2018 | Potential Scenario Ideas

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...

10. 09 Dec 2018 | Potential Scenario Ideas

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...

11. 09 Dec 2018 | Potential Scenario Ideas

Murthy, D. N. P. and E. Y. Rodin. 1987. A comparative evaluation of books on mathematical modeling. Mathematical Modeling. 9(1): 17-28.Abstract: In this paper we present a comparative evaluation of books on mathematical modelling that have appeared in the last 1.5 years.While dated this gives the...

12. 09 Dec 2018 | Potential Scenario Ideas

Cook, K. L. and M. Witten. 1986. One-dimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301-340.Abstract: Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed. Both...

13. 09 Dec 2018 | Potential Scenario Ideas

Cook, K. L. and M. Witten. 1986. One-dimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301-340.Abstract: Some of the results in the literature on simple one-dimensional, density dependent, discrete and continuous models-with and without harvesting-are reviewed. Both...

14. 30 Oct 2018 | Modeling Scenarios

A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

15. 17 Sep 2018 | Modeling Scenarios

We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.

16. 17 Sep 2018 | Modeling Scenarios

We offer several strategies for estimating parameters in models of epidemics, one using a Michaelis-Menten saturation infected rate.

17. 15 Sep 2018 | Modeling Scenarios

We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

18. 15 Sep 2018 | Modeling Scenarios

We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches andusing EXCEL spreadsheet. In this particular modeling scenario, we know the exact solution and want to see how various models predict our expectations. We have used...

19. 30 Aug 2018 | Modeling Scenarios

We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.

20. 30 Aug 2018 | Modeling Scenarios

We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.