This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…

North Korea's development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available…

This article describes the use of a spreadsheet to reinforce basic calculus that is expected of all university-level chemistry majors. The example provided shows a calculation using Excel to estimate, using a Riemann summation, the radiant exitance of a hot object using Planck's Law of Blackbody Radiation. The approach reinforces the elementary…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

Observing the way a watering hose is wrapped on a rotating cylinder, a catenary shape is detected for the suspended portion of the hose. We calculate the angle [alpha] the tangent to the curve at the highest point of the suspended portion makes with the horizontal. By means of this quantity, the length of the suspended and dragged portions of the…

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

Although nowadays there are mythbusting teams ready to empirically confirm or deny advertising claims that may seem too good to be true, it is often economically prohibitive to perform the kinds of experiments that are called for. It is therefore sometimes more sensible and efficacious to perform a thought experiment instead, especially if the…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

Most thermodynamic properties are either extensive (e.g., volume, energy, entropy, amount, etc.) or intensive (e.g., temperature, pressure, chemical potential, mole fraction, etc.). By the same token most of the mathematical relationships in thermodynamics can be written in extensive or intensive form. The basic laws of thermodynamics are usually…

Thermodynamic quantities such as the average energy, heat capacity, and entropy are calculated using a Monte Carlo method based on the Metropolis algorithm. This method is illustrated with reference to the harmonic oscillator but is particularly useful when the partition function cannot be evaluated; an example using a one-dimensional spin system…

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a…

A method is presented to calculate accurate approximations to the half-life values of elimination systems modelled by one compartment. The major advantage of this method is that only algebraic mathematical operations are required. The results will be of value not only to students beginning the study of elimination kinetics, but also to…

Mathematical software packages such as Polymath, MATLAB, and Mathcad are currently widely used for engineering problem solving. Applications of several of these packages to typical chemical engineering problems have been demonstrated by Cutlip, et al. The main characteristic of these packages is that they provide a "problem-solving environment…

The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…