The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

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 paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

This study sought to gather empirical evidence of the effectiveness of calculus instruction like that used in the Calculus and Mathematica project by examining and comparing the effects of three different instructional approaches to calculus on students' (n=100) abilities to use and understand connections between numerical, graphical, and symbolic…

Presented is the work of the calculus group of SMSG. The Advisory Board expressed a desire for a suitable high school calculus text. The calculus group surveyed available texts and, finding none which met advisory board requirements, outlined a suitable course. This outline was annotated for use by future writers. Some group members felt a more…

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

The purpose of this investigation was to examine the interactive effects of prior mathematics preparation and instructional method on achievement in an introductory calculus course taught by both Personalized System of Instruction (PSI) and conventional approaches. Subjects were 248 university students, 60 from the self-paced method and 188 from…

This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…

Presented are the results of a study designed to determine the effect of computer applications on achievement in a college introductory calculus course. Experimental and control classes were compared at each of three participating colleges. The experimental classes solved calculus homework assignments using timesharing remote computer terminals.…

College students' performance in their first two calculus-level mathematics courses was studied by comparing students skipping, on any basis, one or more courses in the regular calculus sequence and students reaching these same courses through the regular sequence. Those skipping via CEEB AP and those skipping for any other reason were also…

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

A method of approximating the point "c" at which a continuous function attains its mean value over an interval is described. The method is applied to tax tables. (SD)

Functions with a variety of properties (sets of discontinuities, unbounded derivations, etc.) are discussed. (SD)

A discussion of differential equations is accompanied by an analysis of two situations whose solutions require differential equations. A computer program is given that will solve these equations. (MP)