In this paper we provide a detailed account of how to implement a peer role model (PRM) program similar to the one that we developed at San Diego State University (SDSU) to broaden participation of college women in science, technology, engineering, and math (STEM). In particular, we summarize our findings of the PRM program's best practices,…

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

Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)

Nonstandard Analysis gives an alternative approach to teaching elementary calculus. This paper hopes to communicate to the reader the ideas of this recent development in mathematics and its implications in teaching undergraduate students. The development of the approach is first briefly traced. Then a method of constructing on ordered field…

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)

This article first appeared in the American Mathematical Monthly in January 1929. In addition to some general concerns, six reasons for lethargic student attitudes are discussed. Stressed is the need to keep mathematics instruction in the hands of teachers prepared to teach mathematics. (MNS)

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

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)

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

A method for teaching the product rule of differentiation in calculus is described. (MK)

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.…