
7011TextSCoupledSystemLaplace
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...

1143SPopulationModelVariationsMATLAB
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...

1003STextIntroNumericalMethods
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.

1063SThreeHoleColumn
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.

2008WillHansenExamplesOfODEsInPhysics
09 Dec 2018  Potential Scenario Ideas
WittHansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

2004PhoebusReilyTheParachuteProblem
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...

1987RodinMurthyComparativeEvalOfMathModelingBooks
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): 1728.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...

1986CookeLinear And Logistic Harvesting ModelsMath Modeling Journal
09 Dec 2018  Potential Scenario Ideas
Cook, K. L. and M. Witten. 1986. Onedimensional linear and logistic harvesting models. Mathematical Modeling. 7: 301340.Abstract: Some of the results in the literature on simple onedimensional, density dependent, discrete and continuous modelswith and without harvestingare reviewed. Both...

6065SInternetPlatformUsers
30 Oct 2018  Modeling Scenarios
A model estimating the volume of users interacting through a twosided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2dimensional dynamical system. The model will illustrate how the question of existence of closed orbits can be investigated....

6019SEnablingEpidemicExploration
17 Sep 2018  Modeling Scenarios
We offer several strategies for estimating parameters in models of epidemics, one using a MichaelisMenten saturation infected rate.

1062SBacterialGrowth
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...

1053SSlimeSpread
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.

6003SSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios
We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

1108SPoissonProcess
27 Aug 2018  Modeling Scenarios
In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

7040STankInterruptMixing
22 Aug 2018  Modeling Scenarios
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.

1067SModelingWithSigmoidCurves
18 Aug 2018  Modeling Scenarios
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1032SDigoxinElimination
17 Aug 2018  Modeling Scenarios
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1130SAspirinAbsorption
15 Aug 2018  Modeling Scenarios
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zeroorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

Kaabar, Mohammed2018A Friendly Introduction to Differential Equations
29 Jul 2018  Free Online Texts
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios
Students will transform, solve, and interpret a tumor growth scenario using nonlinear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...