The author suggests that a close analysis of existing calculus courses indicates that some of the material can be explained much more clearly by using some of the language of set theory. He gives examples showing that many of the pedagogical problems arising in calculus can be overcome by using a graphical approach. (FL)

A program that can reduce difficult integration problems to simpler approximations using the trapezoidal rule to approximate the area under a curve is presented. (MP)

The notion that the area of an inscribed n-sided polygon approaches the area of a circle as n approaches infinity leads to some interesting limits involving trigonometric functions. (MP)

Two problems related to the mean-value theorem lead into a problem requiring the use of the universal chord theorem. This latter theorem is discussed and a proof given. (MP)

An identity for sin x/x is proved. Rate of convergence, a geometric interpretation, and an application from physics are discussed. (DT)

Data from 99 students who completed a microeconomics course indicated that better grades in calculus led to significantly better grades in microeconomics. Higher levels of prior achievement as shown by grade point average correlated with better microeconomics performance. (SK)

Presents examples of using a tic-tac-toe format to practice finding the slope and identifying parallel and perpendicular lines from various equation formats. Reports the successful use of this format as a review in both precalculus and calculus classes before students work with applications of analytic geometry. (JRH)

Documents the experiences of 25 first-year university students with regard to the kinds of tasks calculus instructors should design in order to engage students in mathematical practices that often require the use of a graphing calculator. (MM)

Explains how a microcomputer-based algebra software system, muMATH, can be used to help students understand the theory of convergence of infinite series. Examples are given to illustrate nth term test, ratio test, comparison test, integral test, and Raabe's test. (10 references) (LRW)

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)

Discards the blinders that have hampered the traditional teaching of calculus and reexamines some of the intuitive ideas that underlie this subject matter. Analyzes the various indeterminate forms that arise through the blind application of algebraic operations. (Author/ASK)

Common student attitudes toward reform methods are conveyed through the thoughts of a student leaving a multivariable calculus exam and musings range over textbooks, homework, workload, group work, writing, noncomputational problems, instructional problems, instructional styles, and classroom activities. (Author/ASK)

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)

The Structured Query Language (SQL) forms a substantial component of introductory database courses and is supported by almost every commercial database product. One disadvantage of SQL is that it does not provide a universal quantification construct. Queries that have twisted universal and existential quantifiers can be stunning for students,…

The topic of orthogonal trajectories is taught as a geometric application of first order differential equations. Instructors usually elaborate on the concept of a family of curves to emphasize that they are different even if their members are of the same type. In this article the author considers five families of ellipses, discusses their…