Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We present a new proof of the adiabatic invariance of this quantity and illustrate our arguments by means of…

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)

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)

Investigates the impact of the TI-89 hand-held Computer Algebra System (CAS) on student achievement in a first year college core calculus course. Analyzes data from an experimental study conducted at the United States Military Academy at West Point from 1998-2000. Results indicate that the TI-89 hand-held CAS experimental group attained a higher…

Discusses experiences teaching mathematics courses in a lecture-free, discussion-based seminar format at all levels of the traditional undergraduate mathematics curriculum. Presents methods for motivating, instructing, and supporting student efforts toward independent reading of mathematical text. Provides a non-scientific assessment of the…

Ways to incorporate student mistakes in the instruction of mathematics at the undergraduate level are discussed. A sample investigation of a pupil error with a formula from Calculus is featured. (MP)

States the principal-agent theory is difficult to teach because of its technical complexity and intractability. Indicates the equilibrium in the contract space is defined by the incentive parameter and insurance component of pay under a linear contract. Describes a graphical approach that students with basic knowledge of algebra and…

In July 1982, a conference was held at Williams College in Williamstown, Massachusetts, to discuss the need for more discrete mathematics in the first two years of the core undergraduate mathematics curriculum. This paper reviews the recommendations that were made during the conference, the progress that has been made in the implementation of…

Discusses the rationale for and results of an undergraduate course in calculus using modularized mastery level instruction. The salient features of the present program are instructor controlled learning with modularized materials, immediate results on quizzes, and lecture-recitation sessions. (VT)

Examples are provided of a method of successive approximations suitable for use in a freshman level chemistry course. (CP)

Describes a simple experiment that uses a CCD video camera, a display monitor, and a laser-printed bar pattern to illustrate signal sampling problems that produce aliasing or moiri fringes in images. Uses the Fourier transform to provide an appropriate and elegant means to explain the sampling theorem and the aliasing phenomenon in CCD-based…