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  1. mathematica x
  1. 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...

  2. 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.

  3. 6-012-T-RiverCrossing

    03 Jun 2015 | Modeling Scenarios

    Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential equations. Students must construct a river current...

  4. 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....

  5. 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...

  6. 6-001-T-Epidemic

    03 Jun 2015 | Modeling Scenarios

    This paper presents real-world data, a problem statement, and discussion of a common approach to modeling that data, including student responses.  In particular, we provide time-series data on the number of boys bedridden due to an outbreak of influenza at an English boarding school and ask...

  7. 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.

  8. 4-023-T-MysteryCircuit

    03 Jun 2015 | Modeling Scenarios

    We require students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors in the second loop of the circuit. Students collect the...

  9. 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...

  10. 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...

  11. 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...

  12. 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...

  13. 1-010-T-LSDAndProblemSolving

    02 Jun 2015 | Modeling Scenarios

    We describe the use of  a two compartment model of a linear system of first order linear differential equations to model  lysergic acid diethylamide (LSD) in the body. We provide the data from the literature. We offer students the opportunity to build a two compartment model to fully...

  14. 1-045-T-TimeOfDeath

    02 Jun 2015 | Modeling Scenarios

    Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.

  15. 1-040-T-OutcomeSavings

    02 Jun 2015 | Modeling Scenarios

  16. 1-031-T-CoolIt

    02 Jun 2015 | Modeling Scenarios

  17. 1-009-T-ICUSpread

    02 Jun 2015 | Modeling Scenarios

    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

  18. 1-030-T-IntraocularGasBubbles

    01 Jun 2015 | Modeling Scenarios

    We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina. We ask students to compare the traditional ``empirical'' model used by the...

  19. 1-060-T-SalesMarketing

    01 Jun 2015 | Modeling Scenarios

    We lead students through the development of a sales forecasting model based on marketing principles first espoused by F. M. Bass in 1969. We offer definitions, assumptions, model equations, differential equations, and data on sales over 15 year periods against which   models may be tested.

  20. 1-009-T-Text-Bifurcation

    31 May 2015 | Technique Narratives

    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.