
1026SEvaporation
04 Jun 2015   Contributor(s):: Brian Winkel
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...

1025SMixingItUp
04 Jun 2015   Contributor(s):: Brian Winkel
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.

1023SRumorSpread
04 Jun 2015   Contributor(s):: Brian Winkel
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.

1020SIceMelt
04 Jun 2015   Contributor(s):: Brian Winkel
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.

1018SLogisticPopGrowth
04 Jun 2015   Contributor(s):: Brian Winkel
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.

1017SDiseaseSpread
04 Jun 2015   Contributor(s):: Brian Winkel
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 ...

1016SDogDrugs
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 halflife for an exponentially decaying presence of the drug in the body.

1015STorricelli
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...

1013SSleuthing
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...

1012SSublimationCarbonDioxide
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...

1011SKinetics
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...

1045STimeOfDeath
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.

1040SOutcomeSavings
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.

1031SCoolIt
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...

1009SICUSpread
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 19581974.

1060SSalesMarketing
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.

1030SIntraocularGasBubbles
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, SIMIODESPANISH.cls. Names will be xySTitleStudentVersionSpanish and xyTTitleTeacherVersionSpanish

1007SAntTunnelBuilding
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...

1006SFinancingSavingsAndLoans
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...

1005BSChemDataCollection
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...