Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires…

Describes a technique whereby qualitatively correct models of differentially rotating degenerate stars may be constructed by simple methods available to undergraduate students. (Author/JN)

While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…

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)

Presents simple experiments using the flow of water from bell jars that can provide an easily visualized introduction to exponential decay. (Author)

Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

Describes the spectrum of process design problems. Suggests a methodology for teaching some concepts used in design, including the types of processes considered and their designs, new tools useful in conceptual design, and a strategy for developing conceptual designs. (YP)

Addresses the problem that students balk at the notion velocities do not add algebraically. Offers a geometric model to verify the algebraic formulas that calculate velocity addition. Representations include Galilean relativity, Einstein's composition of velocities, and the inverse velocity transformation. (MDH)

Described is a graduate level engineering course on functional analysis offered at Purdue University. The course restricts itself to linear problems, specifically analysis of linear operators on vector spaces. Key applications in the course demonstrating the utility of abstract formulations are presented. (BT)

Presents a motion problem that students in a college physics class are asked to solve and later asked to continue to analyze until they have stopped learning from the problem or the problem itself is finished. (MDH)

Describes software, hardware, and devices that were designed to provide students with an environment to experiment with basic ideas of mechanics, including nonlinear dynamics. Examines the behavior of a Lorenzian water wheel by comparing experimental data with theoretical results obtained from computer-based sensors. (MDH)

Presents a simple mathematical model in which resultant speed is the sum or difference between wind speed and runner speed and a more complex model that assumes that only a proportion of the wind's speed affects one's running speed to describe the time difference between running with and without wind. (MDH)

Considers several aspects of quantitative relationships involved in learning physics. Includes discussions of proportionality, various kinds of equality, and the need for generality. Argues that clear distinctions are necessary if the physics curriculum is to be examined with regard to pupil outcomes. (TW)