
Browsing Your Way to Better Teaching
31 May 2015  Contributor(s): Brian Winkel
We describe the use of browsing and searching (in libraries, online, inside sources, at meetings, in abstracts, etc.) as a way to stimulate the teacher of undergraduate mathematics, specifically in differential equations. The approach works in all other areas of mathematics. Browsing...

Cross coursing in mathemaitcs: physical modeling in differential equations crossing to discrete dynamical systems
31 May 2015  Contributor(s): Brian Winkel
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modeling in upper level differential equations course into a modest discrete dynamical systems unit of a...

Discover for Yourself: An Optimal Control Model in Insect Colonies
31 May 2015  Contributor(s): Brian Winkel
We describe the enlightening path of selfdiscovery afforded to the teacher of undergraduate mathematics. This is demonstrated as we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum...

Modeling the spread of an oilslick with irregular information
30 May 2015  Articles and Publications  Contributor(s): Brian Winkel
An oilslick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. On each of seven trips the size (in area) of the slick is measured from both...

1005BSChemDataCollection
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel

1005BTChemDataCollection
30 May 2015  Modeling Scenarios  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...

1005ASChemDataCollection
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel

1005ATChemDataCollection
30 May 2015  Modeling Scenarios  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, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of...

1005ATOilSlick
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel

1005ASOilSlick
30 May 2015  Modeling Scenarios  Contributor(s): Karen Bliss

1005TOilSlick
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel
We describe a modeling activity for students in which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...

1005SOilSlick
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel

Population Modeling with M and M's
30 May 2015  Articles and Publications  Contributor(s): Brian Winkel
Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented. Physical activities involving MandM’s can be modeled by difference equations and several population phenomena, including death and immigration, are studied.

1004SMicroorganismImmigration
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel
We present a modeling opportunity for population death with nonconstant immigration and suggest the use of both discrete and continuous models with a comparison of results.

1004TMicroorganismImmigration
30 May 2015  Modeling Scenarios  Contributor(s): Brian Winkel
We present a modeling opportunity for population death with nonconstant immigration and suggest the use of both discrete and continuous models with a comparison of results.

1002TTextIntegratingFactor
30 May 2015  Technique Narratives  Contributor(s): Brian Winkel
A strategy to solve first order differential equations is to transform one side of the differential equation to become the derivative of a product of two functions, thereby making it easy to antidifferentiate that side. This will also transform the other side of the differential...

1002STextIntegratingFactor
30 May 2015  Technique Narratives  Contributor(s): Brian Winkel

1001TTextSeparationOfVariables
30 May 2015  Technique Narratives  Contributor(s): Brian Winkel
We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.

1001STextSeparationOfVariables
30 May 2015  Technique Narratives  Contributor(s): Brian Winkel

1001SMandMDeathAndImmigration
30 May 2015  Modeling Scenarios  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 this...