Using covarient harmonic oscillator formalism as an illustrative example, a method is proposed for illustrating the difference between the Poincare (inhomogeneous Lorentz) and homogeneous Lorentz groups. (BT)

Provides a simplified, synoptic overview of the area of thermodynamics, enumerating and explaining the four basic laws, and introducing the mathematics involved in a stepwise fashion. Discusses such basic tools of thermodynamics as enthalpy, entropy, Helmholtz free energy, and Gibbs free energy, and their uses in problem solving. (JM)

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

Suggests an approach to understanding the integrals associated with teaching electricity and magnetism at the college level. Categorizes integrals that are commonly used, explains the significance of paired usage and presents a method for introducing concepts. Provides a review of symbols and for integrals in college textbooks. (CW)