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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)
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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
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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
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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
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Lutzer, Carl V. – PRIMUS, 2005
Especially in their first upper-division mathematics courses, students often have trouble with proofs; and sometimes they object, "This is hard. I do not get it. Why am I doing this?" Though symptomatic of emotional reaction to difficulty, at its heart this is a legitimate question and it deserves a legitimate answer. This article offers one such…
Descriptors: Mathematics Education, Mathematical Logic, Validity, Emotional Response
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Lutzer, Carl V. – PRIMUS, 2005
Students sometimes have difficulty in mathematics because they solve problems mechanically, without understanding the ideas represented by their equations. This brief note provides mathematics instructors with ideas for rectifying this fundamental flaw in students' paradigm of problem solving. (Contains 1 footnote.)
Descriptors: Numeracy, Thinking Skills, Computation, Teaching Methods
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Lutzer, Carl V. – Primus, 2001
Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)
Descriptors: Calculus, Higher Education, Learning Activities, Mathematics Education