
1109TEmployeeAttrition
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 firstorder linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios
The goal of this project is to set up and numerically solve a firstorder 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...

Mike Karls  Incorporating a Modeling First Approach into a Traditional ODE Course
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, TwoYear College, FourYear Institution at Joint Mathematics Meetings, San Diego CA, 913...

2012KerckhoveMathematica Pop Dynamics Tutorial PDE
10 Sep 2017  Potential Scenario Ideas
Kerckhove, Michael. 2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 118.Abstract: Differential equation models for population dynamics are now standard fare in singlevariable calculus. Building on these ordinary differential equation (ODE)...

2002FayThePendulumEquation
08 Sep 2017  Potential Scenario Ideas
Fay, T. 2001.The Pendulum Equation. Int. J. Math. Educ. Sci. Technology. 33(4): 505519.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 fifthorder Taylor series...

Different Technologies in Use
22 Feb 2016  Articles and Publications
We offer a student posting at the Differential Equations and Fourier Series group found on FaceBook to illustrate the different technologies in use. We believe what follows illustrates the different technologies faculty and students can use and their preferences for many different reasons....

Parameter Estimation
15 Jul 2015  General Resources
We offer a file related to the effort to estimate parameters in differential equation or function models. The file shows the MatLab code and the comparable Mathematica code for the same results.

7005TTextLaplaceTransformOverView
06 Jun 2015  Technique Narratives
The Laplace Transform is a mathematical construct that has proven very useful in both solving and understanding differential equations. We introduce it and show its power here.

3001TSpringMassDataAnalysis
05 Jun 2015  Modeling Scenarios
We offer data on the position of a mass at the end of a spring over time where the spring mass configuration has additional damping due to taped flat index cards at the bottom of the mass. The general modeling of a spring mass configuration and the estimation of parameters form the core of this...

6030TSaltTorricelli
04 Jun 2015  Modeling Scenarios
We build on a model (Torricelli's Law ) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water and the resulting Torricelli's Law model to estimate a parameter in...

1027TStochasticProcesses
04 Jun 2015  Modeling Scenarios
We build the infinite set of first order differential equations for modeling a stochastic process, the socalled 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...

1026TEvaporation
04 Jun 2015  Modeling Scenarios
We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...

1023TRumorSpread
04 Jun 2015  Modeling Scenarios
We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.

1020TIceMelt
04 Jun 2015  Modeling Scenarios
We offer up the claim of a store catalog that its ice ball mold allows users to "... make ice balls that outlast cubes and won't water drinks down." We ask students to build a mathematical model to defend or contradict this claim.

1019TRocksInTheHead
04 Jun 2015  Modeling Scenarios
We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

1018TLogisticPopGrowth
04 Jun 2015  Modeling Scenarios
We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic model in these situations.

1017TDiseaseSpread
04 Jun 2015  Modeling Scenarios
We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways) in a differential equation model for the spread of the disease. Students ...

1017aTDiseaseSpread
04 Jun 2015  Modeling Scenarios
We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways) in a differential equation model for the spread of the disease. Students ...

9012TPDEGuitarTuning
04 Jun 2015  Modeling Scenarios
We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the onedimensional wave equation. We immediately offer numerical solutions in a computer algebra system (we use Mathematica, but any computer...

8002TTextTrigSumRepresentation
04 Jun 2015  Technique Narratives
Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.