One of the main problems in undergraduate research in pure mathematics is that of determining a problem that is, at once, interesting to and capable of solution by a student who has completed only the calculus sequence. It is also desirable that the problem should present something new, since novelty and originality greatly increase the enthusiasm…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

Various ways in which computers can be used in the classroom depending on the subject, students' background, and individual teaching style are discussed. A way to evaluate professional software packages for use in the classroom is included. (KR)