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Lutzer, Carl V. – PRIMUS, 2015

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

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

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