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  1. Population Modeling with M and M's

    30 May 2015 | 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. 

  2. 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...

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

    31 May 2015 | Articles and Publications | 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. Cross coursing in mathemaitcs: physical modeling in differential equations crossing to discrete dynamical systems

    31 May 2015 | Articles and Publications | 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...

  5. Browsing Your Way to Better Teaching

    31 May 2015 | Articles and Publications | 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...

  6. Elementary (My Dear Watson) Differential Equation

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

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  7. Fourier Series: Optimization Opportunity

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

    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.  Specifically, we show how the study of Fourier series can be motivated to enrich a multivariable calculus class. We do this through discovery learning and use...

  8. Informed Conjecturing of Solutions for Differential Equations In a Modeling Context

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

    We examine two differential equations, (1)  first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We...

  9. Sourcing for Parameter Estimation and Study of Logistic Differential Equation

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

    We present two simulation activities for students to generate real data and several data sources for the purpose of estimating parameters in the logistic differential equation model.

  10. Parameter Estimates in Differential Equation Models for Chemical Kinetics

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

    We estimate the parameters present in several differential equation models of (1) chemical reactions of order n where n = 0, 1, 2, (2)  chemical reaction A --> B --> C, and (3) logistic growth model.