The question is addressed of choosing four points on the circumference of an ellipse so that the quadrilateral formed has maximum area. (MP)

Presents an exercise suitable for beginning calculus students that may give insight into series representations and allow students to see some elementary application of these representations. The Fourier series is used to approximate by taking sums of trigonometric functions of the form sin(ns) and cos(nx) for n is greater than or = zero. (PVD)

Error estimates for tangent line approximations and for numerical integration are found using special cases of the error formulas for Taylor's Theorem and the Trapezoidal Rule, respectively. Proofs of these theorems rely on a modification of Rolle's Theorem. (Author/MKR)

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

The method of integration by parts is one of the most useful in integral calculus. Among the most important applications is the integration of differentials involving products, differentials in involving logarithms, and differentials involving inverse circular functions.

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Based on the dominated convergence theorem and parametric differentiation, two different evaluations of the Laplace integral are displayed. This article presents two different proofs of (1) which may be of interest since they are based on principles within the realm of real analysis. The first method applies the dominated convergence theorem to…

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

Finding a periodic solution to a nonlinear ordinary differential equation is in general a difficult task. Only in a very few cases can direct methods be applied to an equation to find initial values leading to a solution of the corresponding initial value problem that is periodic. Oscillatory periodic solutions have such practical importance that…

The idea of cutting out a curve while looking at the direction of cut of the scissors is used to explore concepts related to curves, tangents and derivatives, especially tangent line, concavity and points of inflection, curvature, and a curve as envelope of tangent lines. (Contains 6 figures.)

This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability. (Contains 2 tables and 10 figures.)