We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)

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…

This article shows how highly mobile computing, when used with new forms of network connectivity, can allow new forms of activities in the mathematics classroom. Examples are provided, such as the ability to share, harvest, and aggregate mathematical objects, and the ability for teachers and students to analyze the entire set of classroom…

Since antiquity, ideas regarding true beauty have been usurped by the purview of mathematics. From the aesthetic "logic" of Aristotle to the instrumentalized brutality of the Final Solution and its methodical anthropometric measurements, we see how the symmetry of numbers has been used to quantify the bodily politic according to an empirical…

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

This note describes an interdisciplinary project designed to enhance students' knowledge of the basic techniques taught in a multivariable calculus course. The note discusses the four main requirements of the project and then the solutions for each requirement. Concepts covered include differentials, gradients, Lagrange multipliers, constrained…

This paper concerns the analysis of a didactic engineering, the aim of which is to introduce Calculus, at secondary-school level, through the relationship between global and local points of view. It was designed for a graphic-symbolic calculator environment and structured in accordance with a learning trajectory from identifying the graphical…

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

It is shown how the same physically appealing method can be applied to find analytic solutions for two difficult and apparently unrelated problems in optics and electrostatics. They are: (i) the diffraction of a plane wave at a perfectly conducting thin half-plane and (ii) the electrostatic field associated with a parallel array of stripes held at…

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus…

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

This article describes several ways that calculus students can develop a deeper understanding of related rates by getting actively involved in the lesson.

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…

Prior research across hundreds for introductory physics courses has demonstrated that traditional physics instruction does not generally lead to students learning physics concepts in a meaningful way, but that interactive-engagement physics courses do sometimes promote a great deal more student learning. In this work I analyze a reform effort in a…