Presents a modification of the tabular method for evaluating two types of integrals that requires using the integration-by-parts method twice. (ASK)

The development of the derivative because of being part of calculus in permanent dialectic, demands on one part an analytical, deductive study and on another an application of rochrematic methods, sources of resources, within calculus of derivative which allows to dialectically confront knowledge in its different phases and to test the results.…

Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

A method for teaching the product rule of differentiation in calculus is described. (MK)

Use of the computer program "Integrate Using Definition" can help students develop understanding of integral. Several applications of the program are discussed. (MNS)

This paper demonstrates how calculators may be used to motivate a concept called infinite composition of functions. Several mathematical topics, such as continued square roots, continued fractions, and infinite products are treated and discussed as special cases. (Author/MK)

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…

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

Utilizing composition of elementary functions as prototype of dynamical system, notions of periodic points and their orbits in relation to concept of shift map are used to illustrate concept of continuity. A special case of Sarkovskii's theorem, dealing with period-3 point, is presented with proof relying solely upon Intermediate Value Theorem and…

The author discusses the use of calculators in calculus classes and difficulties caused by roundoff errors. References for advanced follow-up topics are given. (Author/MK)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Presented are five short articles which describe innovations in mathematics teaching. Included are "Polar Summation,""The Age of the Solar System,""Forward Homework--A Motivational Tool,""Trigonometric Identities through Calculus," and "Algorithms for Evaluation of Polynomials." (CW)

Describes a scheme for testing and assisting students with the mathematical skills essential for math courses. Discusses the aims and philosophy of the scheme and describes the logistics of running such a scheme. Reviews student performance and discusses those skills that students are strong in or have difficulty mastering. (Author/ASK)

The approximation of functions such as the sine, cosine, and exponential by polynomials is significant and interesting enough for students to learn about. Presents Maclaurin's theorem, examples employing the theorem, and applications of the theorem. (ASK)