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1-016-S-DogDrugs
04 Jun 2015 | | Contributor(s):: Brian Winkel
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.
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1-015-S-Torricelli
03 Jun 2015 | | Contributor(s):: Brian Winkel
We model the height of a falling column of water in a right circular cylinder (radius = 4.17 cm) emptying through a small hole on the side of the cylinder. Indeed, in all the videos below where are referred to in this Modeling Scenario the cylinder is a 2 liter soda pop...
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1-013-S-Sleuthing
03 Jun 2015 | | Contributor(s):: Brian Winkel
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...
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1-012-S-SublimationCarbonDioxide
03 Jun 2015 | | Contributor(s):: Brian Winkel
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...
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1-011-S-Kinetics
03 Jun 2015 | | Contributor(s):: Brian Winkel
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 offer many opportunities to model these chemical reactions with data, some of which comes from...
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1-045-S-TimeOfDeath
02 Jun 2015 | | Contributor(s):: Brian Winkel
Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.
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1-040-S-OutcomeSavings
02 Jun 2015 | | Contributor(s):: Brian Winkel
We ask students to build a model for a savings account and to determine the monthly deposit in a savings account in order meet a long term savings goal.
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1-031-S-CoolIt
02 Jun 2015 | | Contributor(s):: Brian Winkel
We offer data on the temperature of water in a beaker which resides in a room of constant temperature and also in an environment of nonconstant temperature. Students are encouraged to consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets...
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1-009-S-ICUSpread
02 Jun 2015 | | Contributor(s):: Brian Winkel
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.
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1-060-S-SalesMarketing
01 Jun 2015 | | Contributor(s):: Brian Winkel
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.
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1-030-S-IntraocularGasBubbles
01 Jun 2015 | | Contributor(s):: Brian Winkel
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.cls. Names will be x-y-S-Title-StudentVersion-Spanish and x-y--T-Title-TeacherVersion-Spanish
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1-007-S-AntTunnelBuilding
31 May 2015 | | Contributor(s):: Brian Winkel
We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION We have placed in Supporting Docs both...
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1-006-S-FinancingSavingsAndLoans
31 May 2015 | | Contributor(s):: Brian Winkel
We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...
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1-005B-S-ChemDataCollection
30 May 2015 | | Contributor(s):: Brian Winkel
We present a situation in which a chemistry graduate student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...
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2009-Winkel, Brian - Population Modeling with M and M's
30 May 2015 | | Contributor(s):: Brian Winkel
From Population modelling with M&M's, International Journal of Mathematical Education in Science and Technology, 40(4): 554 — 558. (2009)Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented. Physical activities...
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1-004-S-MicroorganismImmigration
30 May 2015 | | Contributor(s):: Brian Winkel
We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.
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1-001-S-MandMDeathAndImmigration
30 May 2015 | | Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, collect data, estimate parameters, and compare their model prediction with their actual data. There is a video of one run of the main simulation in...
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1-003-S-CollegeSavings
12 May 2015 | | Contributor(s):: Brian Winkel
We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.
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1-002-S-Tossing
11 May 2015 | | Contributor(s):: Brian Winkel
We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.We add a Hand Out Working Version which can be used in class authored by Rachel ...