2010-Kijek, A. and T. Kijek - Modelling of Innovation Diffusion.
02 Sep 2017 | Contributor(s):: Brian Winkel
Kijek, A. and T. Kijek. 2010. Modelling of Innovation Diffusion. Operations Research and Decisions. 3-4:53-68.See https://econpapers.repec.org/article/wutjournl/v_3a3-4_3ay_3a2010_3ap_3a53-68_3aid_3a169.htm .Abstract: Since the publication of the Bass model in 1969, research on the...
26 Aug 2017 | | Contributor(s):: Brian Winkel
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.
15 Aug 2017 | | Contributor(s):: Brian Winkel
We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.
26 Apr 2017 | | Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon
Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...
17 Mar 2017 | | Contributor(s):: Brian Winkel
We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''
30 Nov 2016 | | Contributor(s):: Richard Corban Harwood
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential...
27 Nov 2016 | | Contributor(s):: Brian Winkel
We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.
26 Nov 2016 | | Contributor(s):: Sania Qureshi, Brian Winkel
We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...
23 Nov 2016 | | Contributor(s):: Brian Winkel
We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters.
22 Nov 2016 | | Contributor(s):: Brian Winkel
We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
12 Oct 2016 | | Contributor(s):: Brian Winkel
Two possible multiple dose drug administration regimens are offered for modeling. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and the other involves steady drip flow over short periods of time....
05 Oct 2016 | | Contributor(s):: Brian Winkel
We model the cooling of a baked potato and compare it to student-collected data.
11 Sep 2016 | | Contributor(s):: Dan Flath
We offer students the opportunity to develop several strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t. We go further...
31 Jul 2016 | | Contributor(s):: Brian Winkel
Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.
23 Jul 2016 | | Contributor(s):: Brian Winkel
We offer students a chance to model a one compartment salt mixing model.
27 Jun 2016 | | Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice. Collected data on generation or iteration and population is then...
25 Jun 2016 | | Contributor(s):: Troy Henderson
We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.
22 Jun 2016 | | Contributor(s):: Troy Henderson
We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat. This data can be used to model and predict the amount...
03 Jun 2016 | | Contributor(s):: John Thomas Sieben
Things float or they don’t. Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...
19 May 2016 | | Contributor(s):: John Thomas Sieben
Divers, especially novice divers, have concerns about running out of breathing air while at depth. One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using...