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  1. 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...

  2. 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...

  3. 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...

  4. 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...

  5. 1-025-T-MixingItUp

    04 Jun 2015 | Modeling Scenarios

    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.

  6. 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.

  7. 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,...

  8. 1-016-T-DogDrugs

    04 Jun 2015 | Modeling Scenarios

    We offer a problem of determining the necessary drug administration in order to keep a dogsedated with specific information on half-life for an exponentially decaying presence of the drug in the body.

  9. 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...

  10. 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.

  11. 7-008-T-MachineReplacement

    04 Jun 2015 | Modeling Scenarios

    Students build an integro-differential equation model using a convolution for  machine replacement strategies for two different machine failure models: (1) exponentially distributed failure (student exercise) and (2) fixed time replacement. We discuss all the necessary probability notions...

  12. 6-035-T-Shampoo

    04 Jun 2015 | Modeling Scenarios

    We ask students to model the amount of shampoo in a bottle if when we shower we do not cover the opening at the top of the bottle while in the shower.

  13. 6-008-T-PursuitModels

    03 Jun 2015 | Modeling Scenarios

    Students are prompted to build systems of nonlinear differential equations to model pursuit-evader activities in which a pursuer attempts to follow, perhaps track down and come close to, an evader without knowledge of the evader's intentions, just knowledge of the evader's path history....

  14. 6-005-T-InsectColonyOpt

    03 Jun 2015 | Modeling Scenarios

     We present a system of nonlinear differential equations to model the  control of energy flow into producing workers or reproducers in an insect colony. With a set of given parameters and a number of different  energy  functions we permit students to explore options as to...

  15. 5-005-T-Dialysis

    03 Jun 2015 | Modeling Scenarios

    We guide students through the design of a compartment model of a kidney dialysis machine and compare 3 and 9 compartments for the dialysis machine as well as require students to determine the effect of change in one of the parameters in the model on the effectiveness to deliver quality dialysis.

  16. 1-015-T-Torricelli

    03 Jun 2015 | Modeling Scenarios

    We help students develop 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 offer several sources of simulations on YouTube and at this site from which we collect data and ask students to verify...

  17. 1-013-T-Sleuthing

    03 Jun 2015 | Modeling Scenarios

    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...

  18. 1-012-T-SublimationCarbonDioxide

    03 Jun 2015 | Modeling Scenarios

    We offer data on the sublimation of dry ice (carbon dioxide) with data collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the differential equation, estimate the parameters in...

  19. 1-011-T-Kinetics

    03 Jun 2015 | Modeling Scenarios

    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions and offer many opportunities to model these...

  20. 1-040-T-OutcomeSavings

    02 Jun 2015 | Modeling Scenarios