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Lutzer, Carl V. – PRIMUS, 2011

We propose an alternative to the standard introduction to the derivative. Instead of using limits of difference quotients, students develop Taylor expansions of polynomials. This alternative allows students to develop many of the central ideas about the derivative at an intuitive level, using only skills and concepts from precalculus, and…

Descriptors: Calculus, Mathematics Instruction, Graphs, Information Technology

Lutzer, Carl V. – PRIMUS, 2007

In this article, we discuss an alternative method of teaching students about the Dirac [delta]-function. The method provides students with the mechanical tools they need in order to work with the [delta]-function in practice, while also fostering a sense of cohesion in the calculus curriculum by presenting the [delta]-function as an evolution of…

Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Concepts

Lutzer, Carl V. – PRIMUS, 2006

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Descriptors: Introductory Courses, Equations (Mathematics), Calculus, Algebra