In this thesis, I study some aspects of how students learn to use math to make sense of physical phenomena. Solving physics problems usually requires dealing with algebraic expressions. That can take the form of reading equations you're given, manipulating them, or creating them. It's possible to use equations simply according to formal rules of…

An account of peculiar light patterns produced by reflection in a pool under falling rain droplets was recently reported by Molesini and Vannoni (2008 Eur. J. Phys. 29 403-11). The mathematical approach, however, only covered the case of a symmetrical location of a light source and the observer's eyes with respect to the vertical of the falling…

Derives the general Doppler formula in a nonstatic universe using assumptions of special relativity, homogeneity and isotropy of the universe. Examples of applications to physical cosmology are given. (SL)

By providing an example problem in solving sets of nonlinear algebraic equations, the advantages and disadvantages of two methods for its solution, the tearing approach v the Newton-Raphson approach, are elucidated. (CS)

Develops a graphical method for studying the parallel susceptibility of an antiferromagnetic material. (SL)

Describes the numerical methods of relaxation and over-relaxation for solving Laplace's equation for a system of conductors, and gives several examples of their use. (Author/GA)

Gives a sketch of some topics in distribution theory that is technically simple, yet provides techniques for handling the partial differential equations satisfied by the most important Green's functions in physics. (Author/GA)

A static method of measuring the surface tension of a liquid is presented. Jaeger's method is modified by replacing the pressure source with a variable pressure head. By using this method, stationary air bubbles are obtained thus resulting in controllable external parameters. (Author/KR)

Presents an operator which transforms quantum functions to solve problems of the stationary state wave functions for a particle and the motion and spreading of a Gaussian wave packet in uniform gravitational fields. (SL)

Presents a completely arithmetic development of Newtonian dynamics in which all classical conservation laws are valid and all equations are in forms amenable to high-speed digital computer computation. (SL)

Provides an introduction to Debye potentials and simplified derivations of the multipole expansions of electrodynamic fields. (SL)

Reviews the application of population balance mathematical treatment to transfer operations in chemical engineering. (SL)

Solves the quantum mechanical problem of the bound states corresponding to a sum of several delta-shell potentials. (SL)

A brief introduction to the broad field of curve-fitting is provided to help explain the reasoning behind least-squares data fitting, and also to provide useful equations for two functional forms of interest in chemistry. Appendices give program examples written in Fortran and detail the method of Guggenheim. (MP)