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  1. Browsing Your Way to Better Teaching

    31 May 2015 | Contributor(s): Brian Winkel

    We describe the use of browsing and searching (in libraries, on-line, 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...

  2. 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...

  3. Discover for Yourself: An Optimal Control Model in Insect Colonies

    31 May 2015 | Contributor(s): Brian Winkel

    We describe the enlightening path of self-discovery 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...

  4. Modeling the spread of an oil-slick with irregular information

    30 May 2015 | Articles and Publications | Contributor(s): Brian Winkel

    An oil-slick 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...

  5. 1-005B-S-ChemDataCollection

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

  6. 1-005B-T-ChemDataCollection

    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...

  7. 1-005A-S-ChemDataCollection

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

  8. 1-005A-T-ChemDataCollection

    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...

  9. 1-005A-T-OilSlick

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

  10. 1-005A-S-OilSlick

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

  11. 1-005-T-OilSlick

    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 ...

  12. 1-005-S-OilSlick

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

  13. 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. 

  14. 1-004-S-MicroorganismImmigration

    30 May 2015 | Modeling Scenarios | 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.

  15. 1-004-T-MicroorganismImmigration

    30 May 2015 | Modeling Scenarios | 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.

  16. 1-002-T-Text-IntegratingFactor

    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...

  17. 1-002-S-Text-IntegratingFactor

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

  18. 1-001-T-Text-SeparationOfVariables

    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.

  19. 1-001-S-Text-SeparationOfVariables

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

  20. 1-001-S-MandMDeathAndImmigration

    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...