This is part one of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include: (1) polynomial functions; (2) the derivative of a polynomial function; and…

This is part three of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include area and the integral, differentiation theory and technique, mathematical…

A method is presented for constructing infinite series with prescribed rates of convergence. The method is presented as being an aid to improving the student's understanding of how the partial sum of an infinite series can be used to approximate the sum of the series, as well as being of interest in itself. The focus of the paper is the degree of…

The purpose of the present study was to norm and validate the College-Level Examination Program (CLEP) Introductory Calculus Subject Examination for two University of Illinois calculus courses, Math 120 and Math 135. It was of interest to determine if this examination could be used as a calculus placement and proficiency examination for new…

A general statistical model for the multivariate analysis of mean and covariance structures is described. Matrix calculus is used to develop the statistical aspects of one new special case in detail. This special case separates the confounding of principal components and factor analysis. (DEP)

Graphic displays of elliptic, parabolic, and hyperbolic surfaces can be generated by computers. (SD)

When students were given calculus instruction based on the nonstandard defintion of limit, achievement was comparable to that of a control group using regular text materials. Attitudes of teachers regarding the use of the nonstandard approach are reported. (SD)

A major source of challenging problems for students is the use of higher mathematics to derive elementary problems. Several examples are given. (MP)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

A magazine article is shown to contain material that could lead to discussions of several topics in mathematics. The article and the related mathematics are discussed in detail. (MP)

Performance objectives for precalculus mathematics are listed after a look at the content of current calculus courses. (JT)

The author argues for a more enthusiastic use of mapping diagrams by demonstrating how effective they are in teaching some concepts in calculus. (MN)

Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)

Computer algebra systems are described. Features of such systems and information on MACSYMA, Maple, muMath, REDUCE, and SMP are given. (MNS)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)