We present an approach of defining certain transcendental functions as solutions to initial value problems or systems of such problems. This material is suitable for use in a second-semester one-variable calculus course.

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 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…

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…

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…

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…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

A coin tossed onto a table often ends up rolling in such a way that the center of mass remains approximately stationary. Although this phenomenon has been studied for many years and is well-documented in the literature, it is perhaps not widely appreciated in the physics education community that the motion can be understood without the use of…

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

The purpose of this study was to investigate the effects of motivation, volition and belief change strategies, implemented with personal and group email messages, on students' attitudes, study habits and achievement in a calculus course for non-mathematics majors. Eighty four undergraduates enrolled in a calculus course received emails over a…

This paper introduces a concept of differentiability for functions in several variables which has a very natural definition and shares all the properties one expects of a notion of differentiability, but is shown to be weaker than the usual concept of differentiability defined as local linearizability. The exact connection between the two…

In the usual treatment of waves in introductory courses, one begins with traveling waves and the frequency/wavelength relationship f[lambda] = v, where "v" is the wave velocity. One then makes the point about superposition and shows that two waves traveling in opposite directions can add up to a standing wave; Eq. (1) still applies. This approach…

Several years ago I had to select a new textbook for my calculus-based introductory physics class. I subscribe to Just-in-Time Teaching methods,1 which require students to read the book before the material is covered in class. Thus, the readability of the text by the students is critical. However, I did not feel that I was the best judge of this…