The behavior of certain functions in advanced calculus is discussed, with the mathematics explained. (MNS)

The behavior of some functions near the point of origin is discussed. Each function oscillates, and as x approaches 0, the oscillations become increasingly more rapid; their behavior near the origin improves with increasing values of n. Examples for a calculus class to consider are given. (MNS)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…

Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

A problem that most high school calculus students can explore is presented. It can help students understand such mathematical topics as functional notation, composition of functions, the solving of systems of equations, and the derivative. A computer program is included. (MNS)

Suggests that, for some classes of functions, an algebraic method is available that provides a nonstandard application of the discriminant conditions as well as an exact method of optimization for precalculus students. Examples are given, and students should compare these methods with others regarding generality, ease, and efficiency. (AIM)

Uses parametric equations and a graphing calculator to investigate the connections among the algebraic, numerical, and graphical representations of functions. (MKR)

Presents an activity to introduce the concepts of average rate change and instantaneous rate of change of a function and to explore the relationship between the value of the exponential function and its instantaneous rate of change. (ASK)

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Reports on a study on the construction of examples and counter-examples in a college-level calculus course. Verbal and written productions of the students were classified as one of activity, expression, content, and correctness. Finds two types of strategies, global and local. Analysis also distinguishes between "winning" and…

A definition of convexity with six conditions is discussed and illustrated. (MNS)

This book, written for students of calculus, is designed to augment the explanations of concepts covered in a calculus class. It consists of an overview of calculus divided into basic ideas and vocabulary, the process of differential calculus, and integral calculus. The book is intended as a resource to explain the concepts of calculus in everyday…

Two traditional presentations introducing the calculus of exponential functions are first presented. Then the suggested direct presentation using calculators is described. (MNS)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)