The purpose of this study was to determine if the use of a graphical teaching and learning approach via the graphing calculator enhances students' understanding of the formal definition of limit. College students in six sections of Calculus I participated by completing a test prior to the introduction of the definition, and completing a second…

Despite increases in the representation of African American and Hispanic youth in advanced math courses in high school over the past two decades, recent national reports indicate that substantial inequality in achievement remains. These inequalities can temper one's optimism about the degree to which the United States has made real progress toward…

Although dogs seemingly follow the optimal path where they get to a ball thrown into the water, they certainly do not know the minimization function proposed in the calculus books. Trading the optimization problem for a related rates problem leads to a mathematically identical solution, which, it is argued here, is a more plausible model for the…

Using the problem of determining where a Flatland artist was standing, this article takes another look at perspective.

What may have been the birth of a new calculus problem took place when the author noticed that two coffee cups, one convex and one concave, fit nicely together, and he wondered which held more coffee. The fact that their volumes were about equal led to the topic of this article: complementary surfaces of revolution with equal volumes.

This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.

The paper reports on studies of the impact of harvesting on a prey-predator system with non-monotonic functional response and intra-specific competition in the predator growth dynamics. The existence of its steady states and their stability are studied using eigenvalue analysis. The possibility of the existence of bionomic equilibria has been…

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

This note considers functions of two variables which are continuous on a possibly unbounded closed region in [vertical bar]R[squared], and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is investigated, as are connections with joint density and marginal…

Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical…

One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

An introduction to hypothesis testing using a mathematician's claim that his dog knows calculus and can intuit a minimum path.

This article describes explorations using The Geometer's Sketchpad for algebra and calculus content.

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless…