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  1. mathematica x
  1. 1-109-T-EmployeeAttrition

    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 first-order linear decay model with two populations. This is intended for introductory students and is paired well with exponential growth/decay...

  2. 6-070-T-BeerBubbles

    24 Apr 2018 | Modeling Scenarios

    The goal of this project is to set up and numerically solve a first-order 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...

  3. 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, Two-Year College, Four-Year Institution at Joint Mathematics Meetings, San Diego CA, 9-13...

  4. 2012-Kerckhove-Mathematica Pop Dynamics Tutorial PDE

    10 Sep 2017 | Potential Scenario Ideas

    Kerckhove, Michael.  2012. From Population Dynamics to Partial Differential Equations. The Mathematica Journal. 14: 1-18.Abstract: Differential equation models for population dynamics are now standard fare in single-variable calculus. Building on these ordinary differential equation (ODE)...

  5. 2002-Fay-ThePendulumEquation

    08 Sep 2017 | Potential Scenario Ideas

    Fay, T. 2001.The Pendulum Equation.  Int. J. Math. Educ. Sci. Technology.  33(4): 505-519.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 fifth-order Taylor series...

  6. 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....

  7. 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.

  8. 7-005-T-Text-LaplaceTransformOverView

    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.

  9. 3-001-T-SpringMassDataAnalysis

    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...

  10. 6-030-T-SaltTorricelli

    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...

  11. 1-027-T-StochasticProcesses

    04 Jun 2015 | Modeling Scenarios

    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...

  12. 1-026-T-Evaporation

    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...

  13. 1-023-T-RumorSpread

    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.

  14. 1-020-T-IceMelt

    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.

  15. 1-019-T-RocksInTheHead

    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,...

  16. 1-018-T-LogisticPopGrowth

    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. 

  17. 1-017-T-DiseaseSpread

    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 ...

  18. 1-017a-T-DiseaseSpread

    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 ...

  19. 9-012-T-PDEGuitarTuning

    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 one-dimensional wave equation. We immediately offer  numerical solutions in a computer algebra system (we use Mathematica, but any computer...

  20. 8-002-T-Text-TrigSumRepresentation

    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.