By the time physics students receive their PhDs, they have a broad understanding of many areas of physics and in-depth knowledge in a specific subfield. They have developed a comprehensive knowledge of mathematics, modeling, and programming. Graduate students in physics also develop skills in areas not specifically related to physics and not…

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…

In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

The number of American versus foreign-born students studying mathematics, engineering, and physics in U.S. graduate schools is declining. A program developed at Texas Tech University's Department of Mathematics offers courses in these areas to high-ability secondary-school students, to acquaint them with career opportunities and exciting…