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Winkel, Brian – PRIMUS, 2015

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) 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 follow with a discussion of the complete analysis afforded by…

Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Equations (Mathematics)

Winkel, Brian – PRIMUS, 2013

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 can help build new and refreshing teaching materials based on…

Descriptors: College Mathematics, Mathematics Instruction, Mathematics Teachers, Undergraduate Study

Winkel, Brian – PRIMUS, 2013

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 number of queen or reproducer insects in the colony at…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Entomology

Myers, Joseph; Trubatch, David; Winkel, Brian – PRIMUS, 2008

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Descriptors: Equations (Mathematics), Calculus, Teaching Methods, Mathematical Models