Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…

As an often recommended but under-utilized pedagogical strategy, writing in mathematics has many benefits for students. However, creating and grading worthwhile writing projects can be more time-consuming than utilizing more traditional forms of assessment. This paper provides a concrete example of a writing project prompt, questions, directions,…

In many post-secondary, introductory mathematics courses failure and withdrawal rates are reaching as high as 50% and average GPA is steadily decreasing. This is a problem that has been witnessed across the globe. With widespread reforms taking place in K-12 mathematics education, many innovative teaching strategies have been created, implemented,…

The question is addressed of choosing four points on the circumference of an ellipse so that the quadrilateral formed has maximum area. (MP)

Reasons for using Rolle's Theorem in calculus are discussed, with comparisons to the theorems of Lagrange and Cauchy. (MNS)

The behavior of certain functions in advanced calculus is discussed, with the mathematics explained. (MNS)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

The behavior of some functions near the point of origin is discussed. Each function oscillates, and as x approaches 0, the oscillations become increasingly more rapid; their behavior near the origin improves with increasing values of n. Examples for a calculus class to consider are given. (MNS)

This note presents a simple theorem which explains why the method of undetermined coefficients works in finding a particular solution, both for differential equations and difference equations. (Author)

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

A discrete version of L'Hopital's Rule is presented, with a proof. This version enables one to evaluate the limit and handle other similar problems. (MNS)

Presents a murder mystery in the form of five Calculus I worksheets in which students must apply mathematics to determine which of the suspects committed the murder. Concludes that effort was made to create scenarios that realistically lend themselves to the use of mathematics. (Author/ASK)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…

This article provides three examples from elementary calculus concerning the use of the long ago popular method of parametric differentiation as an alternative form of solution. Included are a partial fraction decomposition, an indefinite integral solution, and an integration by parts. (JJK)