The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

A small class of functions is described that easily lend themselves to two-dimensional and three-dimensional visualizations at the basic calculus level. The intended audience is those educators involved in the instruction of elementary calculus. This note is an educational piece that begins with the question: "What happens if a function defined on…

Discusses a way to help children retain the desire to understand mathematical ideas and to carry out routine procedures. Describes a method using computers to teach linear equations and calculus. Eight references are listed. (YP)

Illustrates how muMATH can be used for manipulating abstract differentiation rules, optimization, implicit differentiation, related rules, and verifying the chain rule. (MVL)

Presents a case study of the design and production of "Interactive Calculus," an interactive multimedia textbook. Discusses reasons for using multimedia textbooks; what an interactive textbook is; content, organization, graphic design, authoring and composition; and work flow. (AEF)

Discusses the snowflake curve as a way to introduce the topic of sequences and series. Computer programs which produce graphic results are included. (PK)

Discusses the use of computers in calculus classes. Describes activities in four laboratories providing with the problems of the laboratories. (YP)

At some point in their education, pre-engineering students will take physics and/or calculus. For many freshmen who aren't certain about their career paths, taking these courses is a litmus test to determine whether they have the aptitude or desire to pursue an engineering degree. Therein lies the challenge for many students in the U.S. Science,…

Explains graphing functions when using LOTUS 1-2-3. Provides examples and explains keystroke entries needed to make the graphs. Notes up to six functions can be displayed on the same set of axes. (MVL)

Describes three software packages: (1) "MacMendeleev"--database/graphic display for chemistry, grades 10-12, Macintosh; (2) "Geometry One: Foundations"--geometry tutorial, grades 7-12, IBM; (3) "Mathematics Exploration Toolkit"--algebra and calculus tutorial, grades 8-12, IBM. (MVL)

Presents several ways that the microcomputer can be used as an aid in teaching various topics in calculus, including graphing functions, solving equations, finding limits and derivatives, and solving optimization problems. Emphasizes the use of computer software that tends to maximize the potential of computer graphics in mathematics instruction.…

This report examines mathematical graphing utilities or function plotters for use in introductory algebra classes of more advanced courses. Each product selected for inclusion in this report is able to construct the graph of a given equation on the screen and serves as a utility which may be used by the student for an open-ended exploration of a…