Everyone with a thorough knowledge of single variable calculus knows that integration can be used to find the length of a curve on a given interval, called its arc length. Fortunately, if one endeavors to pose and solve more interesting problems than simply computing lengths of various curves, there are techniques available that do not require an…

The goals of this note are to derive formulas for the coefficients a and b in the least-squares regression plane y = at + bx + c for observations (t[subscript]i,x[subscript]i,y[subscript]i), i = 1, 2, ..., n, and to present meanings for the coefficients a and b. In this note, formulas for the coefficients a and b in the least-squares fit are…

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…

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…

Describes how the cubic formula can be presented easily at the precalculus level, shows how to verify that the formula is correct, and identifies when it is profitable to use. (KHR)

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

Described is a computer algebra system that can be used to help students understand the calculus. Provides several examples of solving calculus problems using muMATH. Lists eight references. (YP)