Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…

Application of the integral calculus to predicting supplies of oil in future years is described. (SD)

The aims of the study were to explore the effects of teaching heuristics in a calculus course and to generate hypotheses about related changes in heuristic usage and problem solving performance. Thirty college students in two classes participated and a Solomon four-group research design was used. Students from one group in each class were…

This paper describes the nature and use of a computer-assisted sequence of instruction in college-level mathematics. Units in differential and integral calculus and geometry are described. The authors claim that students acquire increased confidence in their knowledge and problem-solving ability. (SD)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

A slight rewording can often transform a routine exercise into a nonroutine one. Three problems (with solutions) from first-year college calculus are presented to illustrate how the technique can be used and how it is applicable to any course. (JN)

In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional…

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

Ways to incorporate student mistakes in the instruction of mathematics at the undergraduate level are discussed. A sample investigation of a pupil error with a formula from Calculus is featured. (MP)

Gives a sketch of some topics in distribution theory that is technically simple, yet provides techniques for handling the partial differential equations satisfied by the most important Green's functions in physics. (Author/GA)

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Describes the problem-solving behaviors of six novice subjects attempting to solve an electrostatics problem in calculus-based college physics. The level of qualitative thinking exhibited by these novices was determined. Sound procedural knowledge and problem representation were suggested as an integral part of skilled problem solving in physics.…

Using a physical picture, an expression for the maximum possible transverse velocity and orientation required for that by a linear emitter in special theory of relativity has been derived. A differential calculus method is also used to derive the expression. (Author/KR)